Estimate the solution to the system of these linear equations based on the graph. y=5x+10 y=−2x+3

1 answer

To estimate the solution to the system of the linear equations \( y = 5x + 10 \) and \( y = -2x + 3 \), we need to find the point where these two lines intersect.

  1. Set the equations equal to each other since they both equal \( y \): \[ 5x + 10 = -2x + 3 \]

  2. Solve for \( x \):

    • Add \( 2x \) to both sides: \[ 5x + 2x + 10 = 3 \] \[ 7x + 10 = 3 \]
    • Subtract 10 from both sides: \[ 7x = 3 - 10 \] \[ 7x = -7 \]
    • Divide by 7: \[ x = -1 \]
  3. Substitute \( x = -1 \) into one of the original equations to find \( y \). We'll use \( y = 5x + 10 \): \[ y = 5(-1) + 10 \] \[ y = -5 + 10 \] \[ y = 5 \]

The solution to the system of equations, which is the point of intersection, is: \[ \boxed{(-1, 5)} \]

If you were to graph these equations, you would see that their lines intersect at the point \((-1, 5)\).