Question

Solving Systems of Equations by Graphing Practice
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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

Answer 1

To estimate the intersection point of the two linear equations given:

1. **Equation of the solid line:** \( y = -x + 7 \)
2. **Equation of the dotted line:** \( y = 4x - 3 \)

From your description, the intersection point of the two lines is given as \( (2, 5) \).

You can confirm the intersection by substituting \( x = 2 \) into both equations:

For the first equation:
\[
y = -2 + 7 = 5
\]

For the second equation:
\[
y = 4(2) - 3 = 8 - 3 = 5
\]

Since both equations yield \( y = 5 \) when \( x = 2 \), we can verify that the two lines indeed intersect at the point \( (2, 5) \).

Therefore, the intersection point of the graphs of the equations \( y = -x + 7 \) and \( y = 4x - 3 \) is \( (2, 5) \).