Question 1

Determine whether the ordered pair is a solution of the system of linear equations
$( 1 , - 3 ) , \left\{ \begin{array} { l } 
2 x + y = - 1 \
4 x + 2 y = - 2
\end{array} \right.$
A) Yes
B) No

Accepted Answer

The ordered pair (1, -3) satisfies both equations. Substituting x = 1 and y = -3 into the first equation yields $2(1) + (-3) = 2 - 3 = -1$, and into the second equation yields $4(1) + 2(-3) = 4 - 6 = -2$, which matches the given equations.

Question 2

Solve the system of equations by the substitution method.
-$$\left\{ \begin{array} { r r } 
x + 6 y & = 7 \
- 4 x + 7 y & = - 28
\end{array} \right.$$
A) $( - 7 , - 1 )$
B) $( 7,0 )$
C) $( 8,7 )$
D) $\varnothing$

Accepted Answer

B

Question 3

Solve the system of equations by the elimination method.
-$$\left\{ \begin{array} { l } 
8 x + 6 y = 32 \
2 x + 6 y = 62
\end{array} \right.$$
A) $( - 5,12 )$
B) $( 8 , - 12 )$
C) $( 6 , - 12 )$
D) $\varnothing$

Accepted Answer

Subtract the second equation from the first equation to get $6x = -30$, so $x = -5$. Substitute this value of $x$ into the second equation to get $2(-5) + 6y = 62$, so $y = 12$. Therefore, the solution to the system of equations is $x = -5$ and $y = 12$, which is choice A.

Question 4

$\left\{\begin{array}{l}
2 x+y=1 \
2 x+y=3
\end{array}\right.$

A) $( 1,3 )$
B) $\left( \frac { 1 } { 2 } , 0 \right)$
C) $\left( \frac { 3 } { 2 } , 0 \right)$
D) $\varnothing$

Accepted Answer

The answer of $\left\{\begin{array}{l}
2 x+y=1 \
2 x+y=3
\end{array}\right.$

A) $( 1,3 )$
B)...

Question 5

Solve the system of equations by the elimination method.
-$$\left\{ \begin{array} { r } 
x + 8 y = 35 \
7 x + 7 y = 0
\end{array} \right.$$
A) $( 5,6 )$
B) $( - 5,5 )$
C) $( - 6,6 )$
D) $\varnothing$

Accepted Answer

To solve the system of equations by the elimination method, we can multiply the first equation by 7 to match the coefficients of $x$ in both equations, which gives us $7x + 56y = 245$. Subtracting the second equation $7x + 7y = 0$ from this result eliminates $x$, leading to $49y = 245$, which simplifies to $y = 5$. Substituting $y = 5$ into the first equation $x + 8(5) = 35$ gives $x + 40 = 35$, so $x = -5$. Therefore, the solution is $(-5, 5)$.

Question 6

Solve the system of equations by the elimination method.
-$$\left\{ \begin{array} { r } 
x - 5 y = - 7 \
- 7 x - 5 y = - 71
\end{array} \right.$$
A) $( - 3,8 )$
B) $( 8,3 )$
C) $( 3,8 )$
D) $\varnothing$

Accepted Answer

By adding the two equations, we eliminate $y$ and solve for $x$, finding $x = 8$. Substituting $x = 8$ back into the first equation gives $y = 3$.

Question 7

Solve the system of equations by the substitution method.
-$$\left\{ \begin{array} { r } 
x - \frac { 5 } { 3 } y = - 4 \
- \frac { 7 } { 3 } x + y = \frac { 2 } { 3 }
\end{array} \right.$$
A) $( - 1 , - 3 )$
B) $( 1 , - 3 )$
C) $( - 1,3 )$
D) $( 1,3 )$

Accepted Answer

The answer of Solve the system of equations by the...

Question 8

$\left\{\begin{array}{rr}
6 x+y= & 0 \
-6 x+y= & -12
\end{array}\right.$
 
A) $( - 1 , - 6 )$
B) $( 1,12 )$
C) $( - 1,6 )$
D) $( 1 , - 6 )$

Accepted Answer

The answer of \(\left\{\begin{array}{rr}
6 x+y= & 0 \
-6 x+y= &...

Question 9

Determine whether the ordered pair is a solution of the system of linear equations $( 5,3 ) , \left\{ \begin{array} { l } 
2 x = 13 - y \
3 x = 21 - 2 y
\end{array} \right.$
A) Yes
B) No

Accepted Answer

Substitute the values of x and y into the equations and check if they satisfy both equations.

Question 10

Solve the system of equations by the substitution method.
-$$\left\{ \begin{aligned}
3 x - 4 y & = 32 \
x & = - 4 y
\end{aligned} \right.$$
A) $( - 8 , - 2 )$
B) $( - 2,8 )$
C) $( 8,2 )$
D) $( 8 , - 2 )$

Accepted Answer

The answer of Solve the system of equations by the...

Question 11

Solve the system of equations by the substitution method.
-$$\left\{ \begin{array} { r } 
x + 7 y = 35 \
- 4 x + 8 y = 40
\end{array} \right.$$
A) $( 1,4 )$
B) $( 0,5 )$
C) $( - 5,0 )$
D) $\varnothing$

Accepted Answer

The answer of Solve the system of equations by the...

Question 12

Determine whether the ordered pair is a solution of the system of linear equations
$( 4,3 ) , \left\{ \begin{array} { l } 
4 x + y = 13 \
3 x + 4 y = 0
\end{array} \right.$
A) Yes
B) No

Accepted Answer

Substitute $x = 4$ and $y = 3$ into both equations:  1) $4(4) + 3 = 16 + 3 = 19$, which is not equal to 13.  2) $3(4) + 4(3) = 12 + 12 = 24$, which is not equal to 0.  Thus, the pair $(4,3)$ is not a solution to the system.

Question 13

Solve the system by graphing.
$\left\{\begin{array}{l}
-x+4 y=-16 \
2 x-8 y=8
\end{array}\right.$

A) (-4, -1)
B) (0, -1)
C) (0, -4)
D) $\phi$

Accepted Answer

The answer of Solve the system by graphing.
\(\left\{\begin{array}{l}
-x+4 y=-16 \
2...

Question 14

Solve the system of equations by the substitution method.
-$$\left\{ \begin{array} { l } 
8 x - 5 y = 69 \
2 x + y = 15
\end{array} \right.$$
A) $( 7,0 )$
B) $( 8 , - 1 )$
C) $( 8,0 )$
D) $\varnothing$

Accepted Answer

First, solve the second equation for $y$: $y = 15 - 2x$. Substitute this into the first equation: $8x - 5(15 - 2x) = 69$. Simplify and solve for $x$: $8x - 75 + 10x = 69$, which simplifies to $18x = 144$, giving $x = 8$. Substitute $x = 8$ back into $y = 15 - 2x$ to find $y = -1$. Thus, the solution is $(8, -1)$.

Question 15

Determine whether the ordered pair is a solution of the system of linear equations
$( - 3,5 ) , \left\{ \begin{array} { l } 
x + y = 2 \
x - y = - 8
\end{array} \right.$
A) Yes
B) No

Accepted Answer

Substituting $x = -3$ and $y = 5$ into both equations: For the first equation, $(-3) + 5 = 2$, which is true. For the second equation, $(-3) - 5 = -8$, which is also true. Since the ordered pair satisfies both equations, it is a solution to the system.

Question 16

Solve the system of equations by the substitution method.
-$$\left\{ \begin{array} { r } 
x + y = 6 \
y = 2 x
\end{array} \right.$$
A) $( 2 , - 4 )$
B) $( - 2,4 )$
C) $( - 2 , - 4 )$
D) $( 2,4 )$

Accepted Answer

Substituting $y = 2x$ into the first equation gives $x + 2x = 6$, which simplifies to $3x = 6$. Solving for $x$ gives $x = 2$. Substituting $x = 2$ into $y = 2x$ gives $y = 4$, so the solution is $(2, 4)$.

Question 17

Determine whether the ordered pair is a solution of the system of linear equations
$( 3,3 ) , \left\{ \begin{array} { l } 
x + y = 0 \
x - y = - 6
\end{array} \right.$
A) Yes
B) No

Accepted Answer

Substituting $x = 3$ and $y = 3$ into both equations, the first equation becomes $3 + 3 = 6$, not $0$, and the second equation becomes $3 - 3 = 0$, not $-6$. Thus, the ordered pair does not satisfy both equations.

Question 18

Solve the system of equations by the substitution method.
-$$\left\{ \begin{array} { r } 
x - 5 y = - 10 \
2 x - 6 y = - 8
\end{array} \right.$$
A) $( 4,4 )$
B) $( 5,3 )$
C) $( - 5,4 )$
D) $\varnothing$

Accepted Answer

The answer of Solve the system of equations by the...

Question 19

Solve the system of equations by the substitution method.
-$$\left\{ \begin{array} { l } 
\frac { x } { 7 } - \frac { y } { 8 } = 1 \
\frac { x } { 9 } - y = 8
\end{array} \right.$$
A) $( - 8,0 )$
B) $( 0,8 )$
C) $( 8,0 )$
D) $( 0 , - 8 )$

Accepted Answer

The answer of Solve the system of equations by the...

Question 20

Determine whether the ordered pair is a solution of the system of linear equations
$( - 1 , - 3 ) , \left\{ \begin{array} { l } 
2 \mathrm { x } = - 1 - \mathrm { y } \
3 \mathrm { x } = - 3 - 2 \mathrm { y }
\end{array} \right.$
A) Yes
B) No

Accepted Answer

The answer of Determine whether the ordered pair is a...

Quiz 4: Systems of Equations and Inequalities

Determine whether the ordered pair is a solution of the system of linear equations $( 1 , - 3 ) , \left\{ \begin{array} { l } 2 x + y = - 1 \\4 x + 2 y = - 2\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { r r } x + 6 y & = 7 \\- 4 x + 7 y & = - 28\end{array} \right.$

Solve the system of equations by the elimination method. - $\left\{ \begin{array} { l } 8 x + 6 y = 32 \\2 x + 6 y = 62\end{array} \right.$

$\left\{\begin{array}{l}2 x+y=1 \\2 x+y=3\end{array}\right.$ $\left\{\begin{array}{l} 2 x+y=1 \\ 2 x+y=3 \end{array}\right. A) ( 1,3 ) B) \left( \frac { 1 } { 2 } , 0 \right) C) \left( \frac { 3 } { 2 } , 0 \right) D) \varnothing$

Solve the system of equations by the elimination method. - $\left\{ \begin{array} { r } x + 8 y = 35 \\7 x + 7 y = 0\end{array} \right.$

Solve the system of equations by the elimination method. - $\left\{ \begin{array} { r } x - 5 y = - 7 \\- 7 x - 5 y = - 71\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { r } x - \frac { 5 } { 3 } y = - 4 \\- \frac { 7 } { 3 } x + y = \frac { 2 } { 3 }\end{array} \right.$

$\left\{\begin{array}{rr}6 x+y= & 0 \\-6 x+y= & -12\end{array}\right.$ $\left\{\begin{array}{rr} 6 x+y= & 0 \\ -6 x+y= & -12 \end{array}\right. A) ( - 1 , - 6 ) B) ( 1,12 ) C) ( - 1,6 ) D) ( 1 , - 6 )$

Determine whether the ordered pair is a solution of the system of linear equations $( 5,3 ) , \left\{ \begin{array} { l } 2 x = 13 - y \\3 x = 21 - 2 y\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{aligned}3 x - 4 y & = 32 \\x & = - 4 y\end{aligned} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { r } x + 7 y = 35 \\- 4 x + 8 y = 40\end{array} \right.$

Determine whether the ordered pair is a solution of the system of linear equations $( 4,3 ) , \left\{ \begin{array} { l } 4 x + y = 13 \\3 x + 4 y = 0\end{array} \right.$

Solve the system by graphing. $\left\{\begin{array}{l}-x+4 y=-16 \\2 x-8 y=8\end{array}\right.$ $Solve the system by graphing. \left\{\begin{array}{l} -x+4 y=-16 \\ 2 x-8 y=8 \end{array}\right. A) (-4, -1) B) (0, -1) C) (0, -4) D) \phi$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } 8 x - 5 y = 69 \\2 x + y = 15\end{array} \right.$

Determine whether the ordered pair is a solution of the system of linear equations $( - 3,5 ) , \left\{ \begin{array} { l } x + y = 2 \\x - y = - 8\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { r } x + y = 6 \\y = 2 x\end{array} \right.$

Determine whether the ordered pair is a solution of the system of linear equations $( 3,3 ) , \left\{ \begin{array} { l } x + y = 0 \\x - y = - 6\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { r } x - 5 y = - 10 \\2 x - 6 y = - 8\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } \frac { x } { 7 } - \frac { y } { 8 } = 1 \\\frac { x } { 9 } - y = 8\end{array} \right.$

Determine whether the ordered pair is a solution of the system of linear equations $( - 1 , - 3 ) , \left\{ \begin{array} { l } 2 \mathrm { x } = - 1 - \mathrm { y } \\3 \mathrm { x } = - 3 - 2 \mathrm { y }\end{array} \right.$

Quiz 4: Systems of Equations and Inequalities

Determine whether the ordered pair is a solution of the system of linear equations (1,−3) ,{2x+y=−14x+2y=−2( 1 , - 3 ) , \left\{ \begin{array} { l } 2 x + y = - 1 \\4 x + 2 y = - 2\end{array} \right.(1,−3) ,{2x+y=−14x+2y=−2​

Solve the system of equations by the substitution method. - {x+6y=7−4x+7y=−28\left\{ \begin{array} { r r } x + 6 y & = 7 \\- 4 x + 7 y & = - 28\end{array} \right.{x+6y−4x+7y​=7=−28​

Solve the system of equations by the elimination method. - {8x+6y=322x+6y=62\left\{ \begin{array} { l } 8 x + 6 y = 32 \\2 x + 6 y = 62\end{array} \right.{8x+6y=322x+6y=62​

{2x+y=12x+y=3\left\{\begin{array}{l}2 x+y=1 \\2 x+y=3\end{array}\right.{2x+y=12x+y=3​

Solve the system of equations by the elimination method. - {x+8y=357x+7y=0\left\{ \begin{array} { r } x + 8 y = 35 \\7 x + 7 y = 0\end{array} \right.{x+8y=357x+7y=0​

Solve the system of equations by the elimination method. - {x−5y=−7−7x−5y=−71\left\{ \begin{array} { r } x - 5 y = - 7 \\- 7 x - 5 y = - 71\end{array} \right.{x−5y=−7−7x−5y=−71​

Solve the system of equations by the substitution method. - {x−53y=−4−73x+y=23\left\{ \begin{array} { r } x - \frac { 5 } { 3 } y = - 4 \\- \frac { 7 } { 3 } x + y = \frac { 2 } { 3 }\end{array} \right.{x−35​y=−4−37​x+y=32​​

{6x+y=0−6x+y=−12\left\{\begin{array}{rr}6 x+y= & 0 \\-6 x+y= & -12\end{array}\right.{6x+y=−6x+y=​0−12​

Determine whether the ordered pair is a solution of the system of linear equations (5,3) ,{2x=13−y3x=21−2y( 5,3 ) , \left\{ \begin{array} { l } 2 x = 13 - y \\3 x = 21 - 2 y\end{array} \right.(5,3) ,{2x=13−y3x=21−2y​

Solve the system of equations by the substitution method. - {3x−4y=32x=−4y\left\{ \begin{aligned}3 x - 4 y & = 32 \\x & = - 4 y\end{aligned} \right.{3x−4yx​=32=−4y​

Solve the system of equations by the substitution method. - {x+7y=35−4x+8y=40\left\{ \begin{array} { r } x + 7 y = 35 \\- 4 x + 8 y = 40\end{array} \right.{x+7y=35−4x+8y=40​

Determine whether the ordered pair is a solution of the system of linear equations (4,3) ,{4x+y=133x+4y=0( 4,3 ) , \left\{ \begin{array} { l } 4 x + y = 13 \\3 x + 4 y = 0\end{array} \right.(4,3) ,{4x+y=133x+4y=0​

Solve the system by graphing. {−x+4y=−162x−8y=8\left\{\begin{array}{l}-x+4 y=-16 \\2 x-8 y=8\end{array}\right.{−x+4y=−162x−8y=8​

Solve the system of equations by the substitution method. - {8x−5y=692x+y=15\left\{ \begin{array} { l } 8 x - 5 y = 69 \\2 x + y = 15\end{array} \right.{8x−5y=692x+y=15​

Determine whether the ordered pair is a solution of the system of linear equations (−3,5) ,{x+y=2x−y=−8( - 3,5 ) , \left\{ \begin{array} { l } x + y = 2 \\x - y = - 8\end{array} \right.(−3,5) ,{x+y=2x−y=−8​

Solve the system of equations by the substitution method. - {x+y=6y=2x\left\{ \begin{array} { r } x + y = 6 \\y = 2 x\end{array} \right.{x+y=6y=2x​

Determine whether the ordered pair is a solution of the system of linear equations (3,3) ,{x+y=0x−y=−6( 3,3 ) , \left\{ \begin{array} { l } x + y = 0 \\x - y = - 6\end{array} \right.(3,3) ,{x+y=0x−y=−6​

Solve the system of equations by the substitution method. - {x−5y=−102x−6y=−8\left\{ \begin{array} { r } x - 5 y = - 10 \\2 x - 6 y = - 8\end{array} \right.{x−5y=−102x−6y=−8​

Solve the system of equations by the substitution method. - {x7−y8=1x9−y=8\left\{ \begin{array} { l } \frac { x } { 7 } - \frac { y } { 8 } = 1 \\\frac { x } { 9 } - y = 8\end{array} \right.{7x​−8y​=19x​−y=8​

Determine whether the ordered pair is a solution of the system of linear equations $( 1 , - 3 ) , \left\{ \begin{array} { l } 2 x + y = - 1 \\4 x + 2 y = - 2\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { r r } x + 6 y & = 7 \\- 4 x + 7 y & = - 28\end{array} \right.$

Solve the system of equations by the elimination method. - $\left\{ \begin{array} { l } 8 x + 6 y = 32 \\2 x + 6 y = 62\end{array} \right.$

$\left\{\begin{array}{l}2 x+y=1 \\2 x+y=3\end{array}\right.$ $\left\{\begin{array}{l} 2 x+y=1 \\ 2 x+y=3 \end{array}\right. A) ( 1,3 ) B) \left( \frac { 1 } { 2 } , 0 \right) C) \left( \frac { 3 } { 2 } , 0 \right) D) \varnothing$

Solve the system of equations by the elimination method. - $\left\{ \begin{array} { r } x + 8 y = 35 \\7 x + 7 y = 0\end{array} \right.$

Solve the system of equations by the elimination method. - $\left\{ \begin{array} { r } x - 5 y = - 7 \\- 7 x - 5 y = - 71\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { r } x - \frac { 5 } { 3 } y = - 4 \\- \frac { 7 } { 3 } x + y = \frac { 2 } { 3 }\end{array} \right.$

$\left\{\begin{array}{rr}6 x+y= & 0 \\-6 x+y= & -12\end{array}\right.$ $\left\{\begin{array}{rr} 6 x+y= & 0 \\ -6 x+y= & -12 \end{array}\right. A) ( - 1 , - 6 ) B) ( 1,12 ) C) ( - 1,6 ) D) ( 1 , - 6 )$

Determine whether the ordered pair is a solution of the system of linear equations $( 5,3 ) , \left\{ \begin{array} { l } 2 x = 13 - y \\3 x = 21 - 2 y\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{aligned}3 x - 4 y & = 32 \\x & = - 4 y\end{aligned} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { r } x + 7 y = 35 \\- 4 x + 8 y = 40\end{array} \right.$

Determine whether the ordered pair is a solution of the system of linear equations $( 4,3 ) , \left\{ \begin{array} { l } 4 x + y = 13 \\3 x + 4 y = 0\end{array} \right.$

Solve the system by graphing. $\left\{\begin{array}{l}-x+4 y=-16 \\2 x-8 y=8\end{array}\right.$ $Solve the system by graphing. \left\{\begin{array}{l} -x+4 y=-16 \\ 2 x-8 y=8 \end{array}\right. A) (-4, -1) B) (0, -1) C) (0, -4) D) \phi$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } 8 x - 5 y = 69 \\2 x + y = 15\end{array} \right.$

Determine whether the ordered pair is a solution of the system of linear equations $( - 3,5 ) , \left\{ \begin{array} { l } x + y = 2 \\x - y = - 8\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { r } x + y = 6 \\y = 2 x\end{array} \right.$

Determine whether the ordered pair is a solution of the system of linear equations $( 3,3 ) , \left\{ \begin{array} { l } x + y = 0 \\x - y = - 6\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { r } x - 5 y = - 10 \\2 x - 6 y = - 8\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } \frac { x } { 7 } - \frac { y } { 8 } = 1 \\\frac { x } { 9 } - y = 8\end{array} \right.$