Question

Identify the equation for the red line and the blue line. Then, identify the solution to the system of equations. (3 points)
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1 y=x-3 2
y=-x+3
y=-x+3
(4, 1)
2 (-4, -1)
(-1, 4)
y=-x-3
(4,-1)

Answer 1

To identify the equations for the red line and the blue line, let's analyze the given equations and the provided coordinates.

1. The first equation is:
- \( y = x - 3 \)
- This is a linear equation with a slope of 1 and a y-intercept of -3.

2. The second equation is:
- \( y = -x + 3 \)
- This is a linear equation with a slope of -1 and a y-intercept of 3.

The system of equations we are dealing with is therefore:
1. \( y = x - 3 \)
2. \( y = -x + 3 \)

To find the solution to the system of equations, we can set the two equations equal to each other:

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

Now, we solve for \( x \):

\[
x + x = 3 + 3
\]
\[
2x = 6
\]
\[
x = 3
\]

Next, we substitute \( x = 3 \) back into one of the original equations to find \( y \):
Using \( y = x - 3 \):

\[
y = 3 - 3 = 0
\]

Thus, the solution to the system of equations is:
\[
(3, 0)
\]

### Summary:
- The equation for the red line: \( y = x - 3 \)
- The equation for the blue line: \( y = -x + 3 \)
- The solution to the system of equations: \( (3, 0) \)