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 the 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 6. The equation of the dotted line is y equals x plus 2. The lines intersect at left parenthesis 2 comma 4 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+2


y=−x+6


(1 point)

Answer 1

To find the intersection point of the two equations \( y = x + 2 \) and \( y = -x + 6 \), we set them equal to each other since at the intersection point both equations yield the same \( y \) value for the same \( x \) value.

1. Set the equations equal to each other:
\[
x + 2 = -x + 6
\]

2. Solve for \( x \):
- Add \( x \) to both sides:
\[
x + x + 2 = 6
\]
\[
2x + 2 = 6
\]

- Subtract 2 from both sides:
\[
2x = 4
\]

- Divide by 2:
\[
x = 2
\]

3. Substitute \( x = 2 \) back into one of the original equations to find \( y \):
- Using \( y = x + 2 \):
\[
y = 2 + 2 = 4
\]

Thus, the intersection point of the graphs of the equations \( y = x + 2 \) and \( y = -x + 6 \) is \( (2, 4) \).

So, the answer is: **(2, 4)**.