# How do you solve the following system using substitution?: x – y = 3, 3x – 2y = 3

Oct 24, 2015

color(green)(x = -3
color(green)(y = -6

#### Explanation:

$x - y = 3$

Transposing $y$ to the other side will give us
$x = y + 3$ -----------------(i)

Substituting this value of $x$ in the second equation given, we get

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

$3 y + 9 - 2 y = 3$

$\left(3 y - 2 y\right) + 9 = 3$

$y + 9 = 3$

Transposing 9 to the other side, we get
$y = 3 - 9$
color(green)(y = -6

Substituting this value of $y$ in (i), we get
$x = - 6 + 3$
color(green)(x = -3