To find the intersection point of the two linear equations given, we need to solve them simultaneously.
The equations are:
- \( 2x + y = 15 \)
- \( y = -x + 5 \)
Start by substituting the expression for \(y\) from the second equation into the first equation.
Substituting \(y\) in the first equation: \[ 2x + (-x + 5) = 15 \] Now simplify the equation: \[ 2x - x + 5 = 15 \] This simplifies to: \[ x + 5 = 15 \] Now, isolating \(x\): \[ x = 15 - 5 \] \[ x = 10 \]
Now that we have \(x\), we can find \(y\) by substituting \(x\) back into the second equation: \[ y = -10 + 5 \] \[ y = -5 \]
Thus, the coordinates of the intersection point are \((10, -5)\).
So the correct answer is: \[ (10, -5) \]