Use the image to answer the question.

Question

y = x - 6
y = -x + 4
Review the graphs of a system of two linear equations in two variables: y = x - 6 and y = -x + 4. Find the solution to both equations.
The intersection point is (__).

Answer 1

To find the solution to the system of equations given by \( y = x - 6 \) and \( y = -x + 4 \), we can set the two equations equal to each other since they both equal \( y \):

\[ x - 6 = -x + 4 \]

Now, solve for \( x \):

1. Add \( x \) to both sides: \[ x + x - 6 = 4 \] \[ 2x - 6 = 4 \]

2. Add 6 to both sides: \[ 2x = 10 \]

3. Divide by 2: \[ x = 5 \]

Next, substitute \( x = 5 \) back into either equation to find \( y \). We'll use the first equation:

\[ y = x - 6 \] \[ y = 5 - 6 = -1 \]

So, the solution to the system of equations, which is the intersection point, is:

\[ \text{The intersection point is } (5, -1). \]

Thus, the final answer is: The intersection point is (5, -1).