# How do you solve 3x + 2y = 7 and x - y + 3 = 0  using substitution?

Mar 31, 2017

$y = 3 \frac{1}{5} , x = \frac{1}{5}$

#### Explanation:

$\therefore 3 x + 2 y = 7$---------- (1)

$\therefore x - y + 3 = 0$

$\therefore x - y = - 3$---------(2)

----(2)$\times 3$:

$\therefore 3 x - 3 y = - 9$--------(3)

-----$\left(1\right) - \left(3\right)$ :

$\therefore 3 x + 2 y = 7$
$\therefore 3 x - 3 y = - 9$
$\therefore 5 y = 16$

$\therefore y = \frac{16}{5}$

$\therefore y = 3 \frac{1}{5}$

substitute $y = 3 \frac{1}{5}$ in $\left(2\right)$

$\therefore x - \left(3 \frac{1}{5}\right) = - 3$

$\therefore x = - 3 + 3 \frac{1}{5}$

$\therefore x = \frac{1}{5}$

substitute $y = \frac{16}{5} , x = \frac{1}{5}$ in $\left(1\right)$

$\therefore 3 \left(\frac{1}{5}\right) + 2 \left(\frac{16}{5}\right) = 7$

$\therefore \frac{3}{5} + \frac{32}{5} = 7$

$\therefore \frac{35}{5} = 7$

$\therefore 7 = 7$