Review the graphs of a system of these two linear equations in two variables: y = 4x - 10 and y = -2x + 8 find the solution.

The solution of the system of equation is ____

1 answer

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

\[ 4x - 10 = -2x + 8 \]

Now, we'll solve for \( x \):

  1. Add \( 2x \) to both sides:

\[ 4x + 2x - 10 = 8 \]

\[ 6x - 10 = 8 \]

  1. Add \( 10 \) to both sides:

\[ 6x = 18 \]

  1. Divide both sides by 6:

\[ x = 3 \]

Now that we have \( x \), we can substitute it back into one of the original equations to find \( y \). We'll use \( y = 4x - 10 \):

\[ y = 4(3) - 10 \]

\[ y = 12 - 10 \]

\[ y = 2 \]

So, the solution of the system of equations is:

\[ \boxed{(3, 2)} \]