Solve the System: 2x + y = 10 and x - y = 2 Step-by-Step

To solve the system of equations:

$2x + y = 10$

$x - y = 2$

First, solve the second equation for $x$:

$x = y + 2$

Substitute $x = y + 2$ into the first equation:

$2(y + 2) + y = 10$

Expand and simplify:

$2y + 4 + y = 10$

$3y + 4 = 10$

Subtract 4 from both sides:

$3y = 6$

Divide by 3:

$y = 2$

Substitute $y = 2$ back into $x = y + 2$:

$x = 2 + 2 = 4$

Thus, the solution is:

$x = 4, y = 2$