Question 1

Determine whether the given ordered pair is a solution of the system
-(-4, -2) 4x + y = -14
2x + 4y = 0
A)not a solution
B)solution

Accepted Answer

Substituting x = -4 and y = -2 into both equations, the first equation becomes 4(-4) + (-2) = -16 - 2 = -18, which does not equal -14. The second equation becomes 2(-4) + 4(-2) = -8 - 8 = -16, which does not equal 0. Therefore, (-4, -2) is not a solution to the system.

Question 2

Solve the system by the addition method.
-$$\begin{array} { l } 
x + y = - 6 \
x - y = 12
\end{array}$$
A) $\{ ( 6 , - 9 ) \}$
B) $\{ ( 6,3 ) \}$
C) $\{ ( 3,9 ) \}$
D) $\{ ( 3 , - 9 ) \}$

Accepted Answer

D

Question 3

Solve the system of equations by the substitution method.
-$$\begin{aligned}
y & = 5 x - 4 \
2 y + 6 x & = - 24
\end{aligned}$$
A) $\{ ( - 9 , - 1 ) \}$
B) $\{ ( 1 , - 9 ) \}$
C) $\{ ( - 1 , - 9 ) \}$
D) $\varnothing$

Accepted Answer

Substituting $y = 5x - 4$ into the second equation gives $2(5x - 4) + 6x = -24$, which simplifies to $16x - 8 = -24$. Solving for $x$ gives $x = -1$. Substituting $x = -1$ back into the first equation gives $y = 5(-1) - 4 = -9$. Therefore, the solution is $(-1, -9)$.

Question 4

Solve the system of equations by the substitution method.
-$$\begin{aligned}
- 5 x + 3 y & = - 22 \
x - 5 y & = 0
\end{aligned}$$
A) $\{ ( 5,1 ) \}$
B) $\{ ( 5 , - 1 ) \}$
C) $\{ ( 6,1 ) \}$
D) $\{ ( 1,5 ) \}$

Accepted Answer

From the second equation, $x = 5y$. Substituting $x$ in the first equation gives $y = 1$ and then $x = 5$, so the solution is $\{(5,1)\}$.

Question 5

Determine whether the given ordered pair is a solution of the system
-(4, 5) 4x - y = 21
3x - 4y = 32
A)solution
B)not a solution

Accepted Answer

Substituting x=4 and y=5 into both equations, the first equation becomes 4(4) - 5 = 16 - 5 = 11, which does not equal 21, and the second equation becomes 3(4) - 4(5) = 12 - 20 = -8, which does not equal 32. Therefore, (4, 5) is not a solution to the system.

Question 6

Determine whether the given ordered pair is a solution of the system
-(-6, 2) 4x = -22 - y
2x = -4 - 4y
A)not a solution
B)solution

Accepted Answer

(-6, 2) is a solution to the system of equations.

Question 7

Solve the system of equations by the substitution method.
-$$\begin{array} { l } 
y = 2 x - 6 \
y = 7 x - 7
\end{array}$$
A) $\{ ( 1 , - 4 ) \}$
B) $\left\{ \left( \frac { 1 } { 5 } , - \frac { 28 } { 5 } \right) \right\}$
C) $\left. \left\{ - \frac { 28 } { 5 } , \frac { 1 } { 5 } \right) \right\}$
D) $\varnothing$

Accepted Answer

Since both equations equal y, you can set them equal to each other: $2x - 6 = 7x - 7$. Solving for x gives $x = \frac{1}{5}$. Substituting $x = \frac{1}{5}$ into one of the original equations to find y gives $y = -\frac{28}{5}$. Therefore, the solution is $\left( \frac{1}{5}, -\frac{28}{5} \right)$.

Question 8

Determine whether the given ordered pair is a solution of the system
-(6, -5) 4x - y = 19
3x + 4y = -2
A)solution
B)not a solution

Accepted Answer

Substitute x = 6 and y = -5 into both equations. For the first equation: 4(6) - (-5) = 24 + 5 = 29, which is not equal to 19. Therefore, (6, -5) is not a solution.

Question 9

Determine whether the given ordered pair is a solution of the system
-(-2, 1) 2x = 5 - y
3x = 8 - 2y
A)not a solution
B)solution

Accepted Answer

Substituting x = -2 and y = 1 into both equations shows that neither equation is satisfied, indicating that (-2, 1) is not a solution to the system.

Question 10

Solve the system of equations by the substitution method.
-$$\begin{array} { l } 
y = \frac { 1 } { 4 } x + 5 \
y = \frac { 1 } { 3 } x + 4
\end{array}$$
A) $\{ ( 12,8 ) \}$
B) $\{ ( - 20,0 ) \}$
C) $\{ ( 12 , - 8 ) \}$
D) $\left\{ \left( \frac { 13 } { 4 } , 29 \right) \right\}$

Accepted Answer

To solve the system of equations by substitution, we set the two expressions for $y$ equal to each other: $\frac{1}{4}x + 5 = \frac{1}{3}x + 4$. Solving for $x$, we subtract $\frac{1}{4}x$ from both sides to get $5 - 4 = \frac{1}{3}x - \frac{1}{4}x$, which simplifies to $1 = \frac{1}{12}x$, leading to $x = 12$. Substituting $x = 12$ into either equation to solve for $y$, we get $y = \frac{1}{4}(12) + 5 = 3 + 5 = 8$. Therefore, the solution is $(12, 8)$.

Question 11

Solve the system of equations by the substitution method.
-$- 9 x + y = 5$ 
$- 3 x - 4 y = - 7$
A) $\left\{ \left( - 4 , - \frac { 3 } { 2 } \right) \right\}$
B) $\{ ( 1 , - 1 ) \}$
C) $\left\{ \left( - \frac { 1 } { 3 } , 2 \right) \right\}$
D) $\left\{ \left( \frac { 2 } { 3 } , 11 \right) \right\}$

Accepted Answer

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

Question 12

Solve the system of equations by the substitution method.
-$\begin{aligned}
x + y & = 6 \
y & = 2 x
\end{aligned}$
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 $x = 2$ back into $y = 2x$ gives $y = 4$. Therefore, the solution is $(2, 4)$.

Question 13

Solve the system of equations by the substitution method.
-$$\begin{array} { l } 
5 x + 9 y = 41 \
3 x - 4 y = - 13
\end{array}$$
A) $\{ ( 0,5 ) \}$
B) $\{ ( 1,5 ) \}$
C) $\{ ( 1,4 ) \}$
D) $\varnothing$

Accepted Answer

First, solve the second equation for $x$: $3x = 4y - 13$ or $x = \frac{4y - 13}{3}$. Substitute this expression for $x$ in the first equation: $5(\frac{4y - 13}{3}) + 9y = 41$. Simplify and solve for $y$: $20y - 65 + 27y = 123$, leading to $47y = 188$, so $y = 4$. Substitute $y = 4$ back into $x = \frac{4y - 13}{3}$ to find $x = 1$. Thus, the solution is $(1, 4)$.

Question 14

Solve the system of equations by the substitution method.
-$$\begin{array} { l } 
x - 7 y = - 40 \
4 x - 8 y = - 20
\end{array}$$
A) $\{ ( - 9,8 ) \}$
B) $\{ ( 8,8 ) \}$
C) $\{ ( 9,7 ) \}$
D) $\varnothing$

Accepted Answer

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

Question 15

Determine whether the given ordered pair is a solution of the system
-(1, -4) x + y = -5
X - y = 3
A)not a solution
B)solution

Accepted Answer

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

Question 16

Determine whether the given ordered pair is a solution of the system
-(1, -4) x + y = -3
X - y = 5
A)solution
B)not a solution

Accepted Answer

The ordered pair (1, -4) satisfies both equations: For the first equation, 1 + (-4) = -3, and for the second equation, 1 - (-4) = 5.

Question 17

Determine whether the given ordered pair is a solution of the system
-(5, 6) 4x + y = 26
2x + 4y = 34
A)not a solution
B)solution

Accepted Answer

Substituting x = 5 and y = 6 into both equations: For the first equation, 4(5) + 6 = 20 + 6 = 26, which matches the given value. For the second equation, 2(5) + 4(6) = 10 + 24 = 34, which also matches the given value. Therefore, (5, 6) is a solution to the system.

Question 18

Solve the system of equations by the substitution method.
-$$\begin{array} { l } 
5 x - 3 y = 49 - 5 x \
3 x + 7 y = x + 6 y + 5
\end{array}$$
A) $\left. \left\{ \int \frac { 49 } { 10 } , 0 \right) \right\}$
B) $\{ ( 4 , - 3 ) \}$
C) $\{ ( 4,3 ) \}$
D) $\{ ( 0,49 ) \}$

Accepted Answer

First, simplify the first equation to $10x - 3y = 49$. For the second equation, simplify to $2x + y = 5$. Solve the second equation for $y$: $y = 5 - 2x$. Substitute into the first equation: $10x - 3(5 - 2x) = 49$. Simplify to find $x = 4$. Substitute $x = 4$ back into $y = 5 - 2x$ to find $y = -3$. The solution is $(4, -3)$.

Question 19

Solve the system of equations by the substitution method.
-$\begin{aligned}
- 2 x - 3 y & = - 21 \
x & = - 5 y
\end{aligned}$
A) $\{ ( 16 , - 3 ) \}$
B) $\{ ( 15 , - 3 ) \}$
C) $\{ ( 15,3 ) \}$
D) $\{ ( - 3,15 ) \}$

Accepted Answer

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

Question 20

Solve the system of equations by the substitution method.
-$$2 y = x + 32$$
$2 x + 4 y = 0$
A) $\{ ( 8 , - 16 ) \}$
B) $\{ ( 16,7 ) \}$
C) $\{ ( - 16 , - 8 ) \}$
D) $\{ ( - 16,8 ) \}$

Accepted Answer

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

Quiz 5: Systems of Equations and Inequalities

Determine whether the given ordered pair is a solution of the system -(-4, -2) 4x + y = -14 2x + 4y = 0

Solve the system by the addition method. - $\begin{array} { l } x + y = - 6 \\x - y = 12\end{array}$

Solve the system of equations by the substitution method. - $\begin{aligned}y & = 5 x - 4 \\2 y + 6 x & = - 24\end{aligned}$

Solve the system of equations by the substitution method. - $\begin{aligned}- 5 x + 3 y & = - 22 \\x - 5 y & = 0\end{aligned}$

Determine whether the given ordered pair is a solution of the system -(4, 5) 4x - y = 21 3x - 4y = 32

Determine whether the given ordered pair is a solution of the system -(-6, 2) 4x = -22 - y 2x = -4 - 4y

Solve the system of equations by the substitution method. - $\begin{array} { l } y = 2 x - 6 \\y = 7 x - 7\end{array}$

Determine whether the given ordered pair is a solution of the system -(6, -5) 4x - y = 19 3x + 4y = -2

Determine whether the given ordered pair is a solution of the system -(-2, 1) 2x = 5 - y 3x = 8 - 2y

Solve the system of equations by the substitution method. - $\begin{array} { l } y = \frac { 1 } { 4 } x + 5 \\y = \frac { 1 } { 3 } x + 4\end{array}$

Solve the system of equations by the substitution method. - $- 9 x + y = 5$ $- 3 x - 4 y = - 7$

Solve the system of equations by the substitution method. - $\begin{aligned}x + y & = 6 \\y & = 2 x\end{aligned}$

Solve the system of equations by the substitution method. - $\begin{array} { l } 5 x + 9 y = 41 \\3 x - 4 y = - 13\end{array}$

Solve the system of equations by the substitution method. - $\begin{array} { l } x - 7 y = - 40 \\4 x - 8 y = - 20\end{array}$

Determine whether the given ordered pair is a solution of the system -(1, -4) x + y = -5 X - y = 3

Determine whether the given ordered pair is a solution of the system -(1, -4) x + y = -3 X - y = 5

Determine whether the given ordered pair is a solution of the system -(5, 6) 4x + y = 26 2x + 4y = 34

Solve the system of equations by the substitution method. - $\begin{array} { l } 5 x - 3 y = 49 - 5 x \\3 x + 7 y = x + 6 y + 5\end{array}$

Solve the system of equations by the substitution method. - $\begin{aligned}- 2 x - 3 y & = - 21 \\x & = - 5 y\end{aligned}$

Solve the system of equations by the substitution method. - $2 y = x + 32$ $2 x + 4 y = 0$

Quiz 5: Systems of Equations and Inequalities

Determine whether the given ordered pair is a solution of the system -(-4, -2) 4x + y = -14 2x + 4y = 0

Solve the system by the addition method. - x+y=−6x−y=12\begin{array} { l } x + y = - 6 \\x - y = 12\end{array}x+y=−6x−y=12​

Solve the system of equations by the substitution method. - y=5x−42y+6x=−24\begin{aligned}y & = 5 x - 4 \\2 y + 6 x & = - 24\end{aligned}y2y+6x​=5x−4=−24​

Solve the system of equations by the substitution method. - −5x+3y=−22x−5y=0\begin{aligned}- 5 x + 3 y & = - 22 \\x - 5 y & = 0\end{aligned}−5x+3yx−5y​=−22=0​

Determine whether the given ordered pair is a solution of the system -(4, 5) 4x - y = 21 3x - 4y = 32

Determine whether the given ordered pair is a solution of the system -(-6, 2) 4x = -22 - y 2x = -4 - 4y

Solve the system of equations by the substitution method. - y=2x−6y=7x−7\begin{array} { l } y = 2 x - 6 \\y = 7 x - 7\end{array}y=2x−6y=7x−7​

Determine whether the given ordered pair is a solution of the system -(6, -5) 4x - y = 19 3x + 4y = -2

Determine whether the given ordered pair is a solution of the system -(-2, 1) 2x = 5 - y 3x = 8 - 2y

Solve the system of equations by the substitution method. - y=14x+5y=13x+4\begin{array} { l } y = \frac { 1 } { 4 } x + 5 \\y = \frac { 1 } { 3 } x + 4\end{array}y=41​x+5y=31​x+4​

Solve the system of equations by the substitution method. - −9x+y=5- 9 x + y = 5−9x+y=5 −3x−4y=−7- 3 x - 4 y = - 7−3x−4y=−7

Solve the system of equations by the substitution method. - x+y=6y=2x\begin{aligned}x + y & = 6 \\y & = 2 x\end{aligned}x+yy​=6=2x​

Solve the system of equations by the substitution method. - 5x+9y=413x−4y=−13\begin{array} { l } 5 x + 9 y = 41 \\3 x - 4 y = - 13\end{array}5x+9y=413x−4y=−13​

Solve the system of equations by the substitution method. - x−7y=−404x−8y=−20\begin{array} { l } x - 7 y = - 40 \\4 x - 8 y = - 20\end{array}x−7y=−404x−8y=−20​

Determine whether the given ordered pair is a solution of the system -(1, -4) x + y = -5 X - y = 3

Determine whether the given ordered pair is a solution of the system -(1, -4) x + y = -3 X - y = 5

Determine whether the given ordered pair is a solution of the system -(5, 6) 4x + y = 26 2x + 4y = 34

Solve the system of equations by the substitution method. - 5x−3y=49−5x3x+7y=x+6y+5\begin{array} { l } 5 x - 3 y = 49 - 5 x \\3 x + 7 y = x + 6 y + 5\end{array}5x−3y=49−5x3x+7y=x+6y+5​

Solve the system of equations by the substitution method. - −2x−3y=−21x=−5y\begin{aligned}- 2 x - 3 y & = - 21 \\x & = - 5 y\end{aligned}−2x−3yx​=−21=−5y​

Solve the system of equations by the substitution method. - 2y=x+322 y = x + 322y=x+32 2x+4y=02 x + 4 y = 02x+4y=0

Solve the system by the addition method. - $\begin{array} { l } x + y = - 6 \\x - y = 12\end{array}$

Solve the system of equations by the substitution method. - $\begin{aligned}y & = 5 x - 4 \\2 y + 6 x & = - 24\end{aligned}$

Solve the system of equations by the substitution method. - $\begin{aligned}- 5 x + 3 y & = - 22 \\x - 5 y & = 0\end{aligned}$

Solve the system of equations by the substitution method. - $\begin{array} { l } y = 2 x - 6 \\y = 7 x - 7\end{array}$

Solve the system of equations by the substitution method. - $\begin{array} { l } y = \frac { 1 } { 4 } x + 5 \\y = \frac { 1 } { 3 } x + 4\end{array}$

Solve the system of equations by the substitution method. - $- 9 x + y = 5$ $- 3 x - 4 y = - 7$

Solve the system of equations by the substitution method. - $\begin{aligned}x + y & = 6 \\y & = 2 x\end{aligned}$

Solve the system of equations by the substitution method. - $\begin{array} { l } 5 x + 9 y = 41 \\3 x - 4 y = - 13\end{array}$

Solve the system of equations by the substitution method. - $\begin{array} { l } x - 7 y = - 40 \\4 x - 8 y = - 20\end{array}$

Solve the system of equations by the substitution method. - $\begin{array} { l } 5 x - 3 y = 49 - 5 x \\3 x + 7 y = x + 6 y + 5\end{array}$

Solve the system of equations by the substitution method. - $\begin{aligned}- 2 x - 3 y & = - 21 \\x & = - 5 y\end{aligned}$

Solve the system of equations by the substitution method. - $2 y = x + 32$ $2 x + 4 y = 0$