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 answer

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

  1. Start with the equations: \[ 2x + y = 15 \quad \text{(1)} \] \[ y = -x + 5 \quad \text{(2)} \]

  2. Substitute equation (2) into equation (1): \[ 2x + (-x + 5) = 15 \]

  3. Simplify the equation: \[ 2x - x + 5 = 15 \] \[ x + 5 = 15 \]

  4. Solve for \( x \): \[ x = 15 - 5 = 10 \]

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

  6. Therefore, the coordinates of the intersection point are: \[ (10, -5) \]

So, the solution to the system of equations is: \[ \boxed{(10, -5)} \]