Question

Use the image to answer the question.

An illustration of a coordinate plane with four quadrants shows x and y axes extending from negative 10 to 10 in increments of 1. A solid line and a dotted line with arrows at both the ends intersect each other. The equation of the solid line is y equals negative x plus 7. The equation of the dotted line is y equals 4 x minus 3. The lines intersect at left parenthesis 2 comma 5 right parenthesis which is not plotted as a point.

Estimate the intersection point of the graphs of the following linear equations in two variables.

y=−x+7


y=4x−3


(1 point)
(
)
Remaining Attempts : 3
Skip to navigation

Answer 1

To find the intersection point of the two given equations, we need to solve the system of equations:

1. \( y = -x + 7 \)
2. \( y = 4x - 3 \)

Since both equations equal \( y \), we can set them equal to each other:

\[
-x + 7 = 4x - 3
\]

Now, we'll solve for \( x \):

1. Add \( x \) to both sides:

\[
7 = 5x - 3
\]

2. Add \( 3 \) to both sides:

\[
10 = 5x
\]

3. Divide both sides by \( 5 \):

\[
x = 2
\]

Now we can substitute \( x = 2 \) back into one of the original equations to find \( y \). Let's use the first equation:

\[
y = -2 + 7
\]

\[
y = 5
\]

So, the intersection point of the graphs of the equations \( y = -x + 7 \) and \( y = 4x - 3 \) is:

\[
(2, 5)
\]

Thus, the answer is:

\[
\boxed{(2, 5)}
\]