Answer
$x = 0$, $y = 3$, or $(0,3)$
Work Step by Step
Given:
$3x + 2y = 6$
$3x + 3 = y$
Subtract the second equation, $3x + 3 = y$, from the first, $3x + 2y = 6$:
$3x + 2y - (3x + 3) = 6 - (y)
\\3x + 2y - 3x - 3 = 6 - y$
Combine like terms:
$2y - 3 = 6 - y$
Add $y$ to both sides of the equation:
$3y - 3 = 6$
Add $3$ to both sides of the equation:
$3y = 9$
Divide both sides of the equation by $3$:
$y = 3$
Substitute $y=3$ into first equation:
$3x+2y=6
\\3x + 2(3) = 6
\\3x+6=6$
Subtract $6$ from both sides:
$3x = 0$
Divide both sides by 3:
$x = 0$
Thus, $x = 0$, $y = 3$