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 \( x \):
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Add \( x \) to both sides: \[ x + x - 6 = 4 \] \[ 2x - 6 = 4 \]
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Add 6 to both sides: \[ 2x = 10 \]
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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).