# How do you solve x – y = 3 and 2x + 2y = 2?

Jun 14, 2018

$\left(x , y\right) = \left(2 , - 1\right)$

#### Explanation:

From the first equation, $x = y + 3$. Substitute in to the second:
$2 \left(y + 3\right) + 2 y = 2$. Multiply this out: $2 y + 6 + 2 y = 2$. Collect terms: $4 y = - 4$, so $y = - 1$.

Return to the first equation: $x - \left(- 1\right) = 3$, so $x = 2$.

Jun 14, 2018

$\left(x , y\right) \to \left(2 , - 1\right)$

#### Explanation:

$x - y = 3 \to \left(1\right)$

$2 x + 2 y = 2 \to \left(2\right)$

$\text{from equation } \left(1\right) \to x = 3 + y \to \left(3\right)$

$\text{substitute "x=3+y" into equation } \left(2\right)$

$2 \left(3 + y\right) + 2 y = 2$

$6 + 2 y + 2 y = 2$

$\text{subtract 6 from both sides}$

$4 y = - 4 \Rightarrow y = \frac{- 4}{4} = - 1$

$\text{substitute "y=-1" into equation } \left(3\right)$

$x = 3 - 1 = 2$

$\text{point of intersection } = \left(2 , - 1\right)$
graph{(y-x+3)(y+x-1)=0 [-10, 10, -5, 5]}