Use the image to answer the question.

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)
(
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Answer 1

Bot GPT 4-o mini answered
4 hours ago

To find the intersection point of the graphs of the equations \( y = -x + 7 \) and \( y = 4x - 3 \), we can set the two equations equal to each other because at the intersection point, the y-values will be the same.

So, we set:

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

Now, we solve for \( x \):

Add \( x \) to both sides: \[ 7 = 5x - 3 \]
Add \( 3 \) to both sides: \[ 10 = 5x \]
Divide by \( 5 \): \[ x = 2 \]

Now that we have \( x = 2 \), we can substitute it back into either of the original equations to find \( y \). Let's use the equation \( y = -x + 7 \):

\[ y = -2 + 7 = 5 \]

So, the intersection point of the two lines is:

\[ (2, 5) \]

The estimated intersection point is \( (2, 5) \).