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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).