Question 1

Match the equation of the line with the point it contains and its slope.
-$y = - 5$

Accepted Answer

The equation $y = -5$ represents a horizontal line passing through the point $(0,-5)$. Since the line is horizontal, the slope is 0. The only choice that matches this description is B, which contains the point $(8,-5)$ and has a slope of 0. Choice A has a slope of 0, but the line does not contain the given point.

Question 2

Match the equation of the line with the point it contains and its slope.
-$y + 4 x = 9$

Accepted Answer

To find the slope-intercept form of the equation, we need to isolate y.

\begin{align*}
y + 4x &= 9 \
y &= -4x + 9 \
\end{align*}

So the slope of line is -4.

Now, we can plug in one of the given points and solve for the y-intercept.

\begin{align*}
y &= -4x + b \
-7 &= -4(4) + b \
b &= -7 + 16 \
b &= 9 \
\end{align*}

So the equation of the line is:

\begin{align*}
y &= -4x + 9 \
\end{align*}

This matches choice B: $( 4 , -7 ) , m = - 4$

Question 3

Decide which of the given ordered pairs is a solution of the given system of equations. $$\left( \begin{array} { l } 
3 x + 2 y = 7 \
5 x - y = 29
\end{array} \right)$$

Accepted Answer

Plug in the first ordered pair, (-5,-4), into the system of equations:
$$\left( \begin{array} { l } 
3(-5) + 2(-4) = -15-8=-23\neq 7\
5(-5)-(-4) =-25+4=-21\neq 29
\end{array} \right)$$
Therefore, (-5,-4) is not a solution to the system.
Similarly, for (7,-8):
$$\left( \begin{array} { l } 
3(7) + 2(-8) = 21-16=5\neq 7\
5(7)-(-8) =35+8=43 \neq 29
\end{array} \right)$$
Therefore, (7,-8) is also not a solution to the system.
However, for (5,-4):
$$\left( \begin{array} { l } 
3(5) + 2(-4) = 15-8=7\
5(5)-(-4) =25+4=29
\end{array} \right)$$
Therefore, (5,-4) is a solution to the system.

Question 4

If the graphs of the equations are parallel, then the system is consistent.

Accepted Answer

If the graphs of the equations are parallel, it means they have no points of intersection, indicating the system is inconsistent, as there are no solutions that satisfy both equations simultaneously.

Question 5

Write the equation of the line that satisfies the given condition: contains the point (-1, 1) and is parallel to the line x + 2 y = 3. Simplify your answer as much as possible. Express the final equation in standard form.

Accepted Answer

The answer of Write the equation of the line that...

Question 6

Match the equation of the line with the point it contains and its slope.
-$- 2 x + 7 y = 8$

Accepted Answer

To find the slope $m$ of the line given by the equation $-2x + 7y = 8$, we first rewrite the equation in slope-intercept form, $y = mx + b$. Solving for $y$, we get $7y = 2x + 8$, and then $y = \frac{2}{7}x + \frac{8}{7}$. Thus, the slope $m$ is $\frac{2}{7}$.

Question 7

A system of equations with no solution is called an inconsistent system.

Accepted Answer

This statement is true. An inconsistent system occurs when there are no solutions to the set of equations, meaning they cannot be solved simultaneously.

Question 8

Write the equation of the line that satisfies the given condition: contains the point (4, -2) and is perpendicular to the y axis. Simplify your answer as much as possible. Express the final equation in standard form.

Accepted Answer

The answer of Write the equation of the line that...

Question 9

Write the equation of the line that satisfies the given condition: contains the point (4, -4) and is perpendicular to the line 8 x - 11 y = -2. Simplify your answer as much as possible. Express the final equation in standard form.

Accepted Answer

The answer of Write the equation of the line that...

Question 10

A system of equations in two variables will contain only two equations.

Accepted Answer

A system of equations in two variables can contain any number of equations, not limited to just two. It's the number of variables that is two, not necessarily the number of equations.

Question 11

A dependent sytem of linear equations will have more than one solution.

Accepted Answer

A dependent system of linear equations can have infinitely many solutions, which is more than one solution.

Question 12

Decide which of the given ordered pairs is a solution of the given system of equations. $\left( \begin{array} { l } 
x + y = 2 \
x - y = 6
\end{array} \right)$

Accepted Answer

To check if an ordered pair is a solution of a system of equations, we substitute the values in the equations and see if they are true.

Substituting (4,-2) in the given equations, 
x + y = 2 becomes 4 + (-2) = 2
which is true.

x - y = 6 becomes 4 - (-2) = 6 
which is again true.

Hence, (4,-2) is a solution of the given system of equations.

Question 13

Match the equation of the line with the point it contains and its slope.
-$2 y - 9 x = 16$

Accepted Answer

To find the slope of the line we need to put it in slope-intercept form, which is  y = mx + b. We can rearrange the given equation to this form by solving for y:
\begin{align*}
2y-9x &= 16 \
2y &= 9x + 16 \
y &= \frac{9}{2}x + 8 
\end{align*}

Now we can see that the slope of the line is 9/2.

Next, we need to check which of the given points lie on this line. Let's check the points from choice (B):
\begin{align*}
(-6,-1) &: y =\frac{9}{2} \cdot (-6) + 8 = -13 \
(-4,-10) &: y =\frac{9}{2} \cdot (-4) + 8 = -10 
\end{align*}

We can see that the point (-4,-10) lies on the line, but the point (-6,-1) does not. Therefore, the best choice is (B).

Question 14

Decide which of the given ordered pairs is a solution of the given system of equations. $$\left( \begin{array} { l } 
2 x + y = 12 \
2 x - 3 y = - 4
\end{array} \right)$$

Accepted Answer

To check if an ordered pair is a solution to a system of equations, we substitute the values of the variables into each equation and see if the equations are true. 
For (4,4), we have: 
$2x+y=12$ becomes $2(4)+4=12$, which is true. 
$2x-3y=-4$ becomes $2(4)-3(4)=-4$, which is also true. 
Therefore, (4,4) is a solution to the system of equations.

Question 15

Write the equation of the line that satisfies the given condition: contains the origin and is perpendicular to the line 6 x + 9 y = 4. Simplify your answer as much as possible. Express the final equation in standard form.

Accepted Answer

The answer of Write the equation of the line that...

Question 16

Match the equation of the line with the point it contains and its slope.
-$y = 9 x - 6$

Accepted Answer

In the equation y = 9x - 6, the slope is 9 and the y-intercept is -6. Therefore, choice A matches both the point (0,-6) and the slope of 9. Choice B has the incorrect slope and y-intercept.

Question 17

Decide which of the given ordered pairs is a solution of the given system of equations. $$\left( \begin{array} { l } 
2 x + 3 y = - 4 \
3 x - y = 16
\end{array} \right)$$

Accepted Answer

Substitute the values of x and y from the ordered pair (4, -4) into the equations and check if they satisfy both equations.

Question 18

Decide which of the given ordered pairs is a solution of the given system of equations. $$\left( \begin{array} { l } 
5 x + y = 25 \
5 x - 2 y = 10
\end{array} \right)$$

Accepted Answer

To determine which ordered pair is a solution to the system of equations, substitute the x and y values from each option into both equations and check for validity. For option B, (4, 5), substituting into the first equation gives $5(4) + 5 = 20 + 5 = 25$, which is true. Substituting into the second equation gives $5(4) - 2(5) = 20 - 10 = 10$, which is also true. Therefore, option B is the correct solution.

Question 19

Decide which of the given ordered pairs is a solution of the given system of equations. $$\left( \begin{array} { l } 
4 x + 2 y = - 6 \
3 x - y = 8
\end{array} \right)$$

Accepted Answer

The answer of Decide which of the given ordered pairs...

Question 20

Write the equation of the line that satisfies the given condition: contains the origin and is parallel to the line 10 x + 3 y = -9. Simplify your answer as much as possible. Express the final equation in standard form.

Accepted Answer

The answer of Write the equation of the line that...

Quiz 5: Coordinate Geometry and Linear Systems

Match the equation of the line with the point it contains and its slope. - $y = - 5$

Match the equation of the line with the point it contains and its slope. - $y + 4 x = 9$

Decide which of the given ordered pairs is a solution of the given system of equations. $\left( \begin{array} { l } 3 x + 2 y = 7 \\5 x - y = 29\end{array} \right)$

If the graphs of the equations are parallel, then the system is consistent.

Write the equation of the line that satisfies the given condition: contains the point (-1, 1) and is parallel to the line x + 2 y = 3. Simplify your answer as much as possible. Express the final equation in standard form.

Match the equation of the line with the point it contains and its slope. - $- 2 x + 7 y = 8$

A system of equations with no solution is called an inconsistent system.

Write the equation of the line that satisfies the given condition: contains the point (4, -2) and is perpendicular to the y axis. Simplify your answer as much as possible. Express the final equation in standard form.

Write the equation of the line that satisfies the given condition: contains the point (4, -4) and is perpendicular to the line 8 x - 11 y = -2. Simplify your answer as much as possible. Express the final equation in standard form.

A system of equations in two variables will contain only two equations.

A dependent sytem of linear equations will have more than one solution.

Decide which of the given ordered pairs is a solution of the given system of equations. $\left( \begin{array} { l } x + y = 2 \\x - y = 6\end{array} \right)$

Match the equation of the line with the point it contains and its slope. - $2 y - 9 x = 16$

Decide which of the given ordered pairs is a solution of the given system of equations. $\left( \begin{array} { l } 2 x + y = 12 \\2 x - 3 y = - 4\end{array} \right)$

Write the equation of the line that satisfies the given condition: contains the origin and is perpendicular to the line 6 x + 9 y = 4. Simplify your answer as much as possible. Express the final equation in standard form.

Match the equation of the line with the point it contains and its slope. - $y = 9 x - 6$

Decide which of the given ordered pairs is a solution of the given system of equations. $\left( \begin{array} { l } 2 x + 3 y = - 4 \\3 x - y = 16\end{array} \right)$

Decide which of the given ordered pairs is a solution of the given system of equations. $\left( \begin{array} { l } 5 x + y = 25 \\5 x - 2 y = 10\end{array} \right)$

Decide which of the given ordered pairs is a solution of the given system of equations. $\left( \begin{array} { l } 4 x + 2 y = - 6 \\3 x - y = 8\end{array} \right)$

Write the equation of the line that satisfies the given condition: contains the origin and is parallel to the line 10 x + 3 y = -9. Simplify your answer as much as possible. Express the final equation in standard form.

Quiz 5: Coordinate Geometry and Linear Systems

Match the equation of the line with the point it contains and its slope. - y=−5y = - 5y=−5

Match the equation of the line with the point it contains and its slope. - y+4x=9y + 4 x = 9y+4x=9

Decide which of the given ordered pairs is a solution of the given system of equations. (3x+2y=75x−y=29) \left( \begin{array} { l } 3 x + 2 y = 7 \\5 x - y = 29\end{array} \right) (3x+2y=75x−y=29​)

If the graphs of the equations are parallel, then the system is consistent.

Write the equation of the line that satisfies the given condition: contains the point (-1, 1) and is parallel to the line x + 2 y = 3. Simplify your answer as much as possible. Express the final equation in standard form.

Match the equation of the line with the point it contains and its slope. - −2x+7y=8- 2 x + 7 y = 8−2x+7y=8

A system of equations with no solution is called an inconsistent system.

Write the equation of the line that satisfies the given condition: contains the point (4, -2) and is perpendicular to the y axis. Simplify your answer as much as possible. Express the final equation in standard form.

Write the equation of the line that satisfies the given condition: contains the point (4, -4) and is perpendicular to the line 8 x - 11 y = -2. Simplify your answer as much as possible. Express the final equation in standard form.

A system of equations in two variables will contain only two equations.

A dependent sytem of linear equations will have more than one solution.

Decide which of the given ordered pairs is a solution of the given system of equations. (x+y=2x−y=6) \left( \begin{array} { l } x + y = 2 \\x - y = 6\end{array} \right) (x+y=2x−y=6​)

Match the equation of the line with the point it contains and its slope. - 2y−9x=162 y - 9 x = 162y−9x=16

Decide which of the given ordered pairs is a solution of the given system of equations. (2x+y=122x−3y=−4) \left( \begin{array} { l } 2 x + y = 12 \\2 x - 3 y = - 4\end{array} \right) (2x+y=122x−3y=−4​)

Write the equation of the line that satisfies the given condition: contains the origin and is perpendicular to the line 6 x + 9 y = 4. Simplify your answer as much as possible. Express the final equation in standard form.

Match the equation of the line with the point it contains and its slope. - y=9x−6y = 9 x - 6y=9x−6

Decide which of the given ordered pairs is a solution of the given system of equations. (2x+3y=−43x−y=16) \left( \begin{array} { l } 2 x + 3 y = - 4 \\3 x - y = 16\end{array} \right) (2x+3y=−43x−y=16​)

Decide which of the given ordered pairs is a solution of the given system of equations. (5x+y=255x−2y=10) \left( \begin{array} { l } 5 x + y = 25 \\5 x - 2 y = 10\end{array} \right) (5x+y=255x−2y=10​)

Decide which of the given ordered pairs is a solution of the given system of equations. (4x+2y=−63x−y=8) \left( \begin{array} { l } 4 x + 2 y = - 6 \\3 x - y = 8\end{array} \right) (4x+2y=−63x−y=8​)

Write the equation of the line that satisfies the given condition: contains the origin and is parallel to the line 10 x + 3 y = -9. Simplify your answer as much as possible. Express the final equation in standard form.

Match the equation of the line with the point it contains and its slope. - $y = - 5$

Match the equation of the line with the point it contains and its slope. - $y + 4 x = 9$

Decide which of the given ordered pairs is a solution of the given system of equations. $\left( \begin{array} { l } 3 x + 2 y = 7 \\5 x - y = 29\end{array} \right)$

Match the equation of the line with the point it contains and its slope. - $- 2 x + 7 y = 8$

Decide which of the given ordered pairs is a solution of the given system of equations. $\left( \begin{array} { l } x + y = 2 \\x - y = 6\end{array} \right)$

Match the equation of the line with the point it contains and its slope. - $2 y - 9 x = 16$

Decide which of the given ordered pairs is a solution of the given system of equations. $\left( \begin{array} { l } 2 x + y = 12 \\2 x - 3 y = - 4\end{array} \right)$

Match the equation of the line with the point it contains and its slope. - $y = 9 x - 6$

Decide which of the given ordered pairs is a solution of the given system of equations. $\left( \begin{array} { l } 2 x + 3 y = - 4 \\3 x - y = 16\end{array} \right)$

Decide which of the given ordered pairs is a solution of the given system of equations. $\left( \begin{array} { l } 5 x + y = 25 \\5 x - 2 y = 10\end{array} \right)$

Decide which of the given ordered pairs is a solution of the given system of equations. $\left( \begin{array} { l } 4 x + 2 y = - 6 \\3 x - y = 8\end{array} \right)$