Review the graphs of a system of

these two linear equations in two
variables: y=4x−10 and y=−2x+8
Find the solution of the system.
(2 points)

1 answer

To find the solution to the system of equations given by \( y = 4x - 10 \) and \( y = -2x + 8 \), we can set the two equations equal to each other since both are equal to \( y \).

  1. Set the equations equal: \[ 4x - 10 = -2x + 8 \]

  2. Solve for \( x \): \[ 4x + 2x = 8 + 10 \] \[ 6x = 18 \] \[ x = 3 \]

  3. Now substitute \( x = 3 \) back into either of the original equations to find \( y \). We'll use the first equation: \[ y = 4(3) - 10 \] \[ y = 12 - 10 \] \[ y = 2 \]

Thus, the solution to the system of equations is \( (3, 2) \).

In summary:

  • The solution of the system is \( (3, 2) \).