To find the solution of the system of equations given by \( y = 4x - 10 \) and \( y = -2x + 8 \), we can set the two equations equal to each other since they both equal \( y \).
-
Set the equations equal to each other: \[ 4x - 10 = -2x + 8 \]
-
Now, solve for \( x \). First, add \( 2x \) to both sides: \[ 4x + 2x - 10 = 8 \] \[ 6x - 10 = 8 \]
-
Next, add \( 10 \) to both sides: \[ 6x = 18 \]
-
Now, divide by \( 6 \): \[ x = 3 \]
-
Now that we have \( x \), substitute back into one of the equations to find \( y \). We'll use the second equation for this: \[ y = -2(3) + 8 \] \[ y = -6 + 8 \] \[ y = 2 \]
The solution to the system of equations is \( (x, y) = (3, 2) \).
Thus, the solution of the system is: \[ \boxed{(3, 2)} \]