Question

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 . (1 point) Responses (10,−5) left parenthesis 10 comma negative 5 right parenthesis (−5, 10) left parenthesis negative 5 comma 10 right parenthesis (5,−10) left parenthesis 5 comma negative 10 right parenthesis (−10, 5)

Answer 1

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

1. Substitute \(y = -x + 5\) into \(2x + y = 15\): \[ 2x + (-x + 5) = 15 \] Simplifying this gives: \[ 2x - x + 5 = 15 \] \[ x + 5 = 15 \] \[ x = 15 - 5 \] \[ x = 10 \]

2. Now substitute \(x = 10\) back into the equation \(y = -x + 5\) to find \(y\): \[ y = -10 + 5 \] \[ y = -5 \]

Thus, the coordinates of the intersection point are \((10, -5)\).

The correct response is \((10, -5)\).