Use the image to answer the question.

y = -x + 5
2x + y = 15
Find the coordinates of the intersection point that solves the system of these two linear equations in two variables: 2x + y = 15 and y = -x + 5.
A. (-5, 10)
B. (-10, 5)
C. (10, -5)
D. (5, -10)

1 answer

To find the coordinates of the intersection point of the two equations \(y = -x + 5\) and \(2x + y = 15\), we can substitute the expression for \(y\) from the first equation into the second equation.

Starting with the second equation: \[ 2x + y = 15 \] Substituting \(y = -x + 5\) into this equation: \[ 2x + (-x + 5) = 15 \]

Now, simplify the equation: \[ 2x - x + 5 = 15 \] \[ x + 5 = 15 \] Subtract 5 from both sides: \[ x = 10 \]

Next, substitute \(x = 10\) back into the first equation to find \(y\): \[ y = -x + 5 \] \[ y = -10 + 5 \] \[ y = -5 \]

Thus, the intersection point is \((10, -5)\).

Therefore, the answer is: C. (10, -5)