# How do solve the following linear system?:  x+2y =2 , x - 3y = -6 ?

Dec 28, 2015

Using substitution I have found the answer below.

#### Explanation:

x + 2y = 2
x = 2 - 2y
2 - 2y - 3y = -6
2 - 5y = -6
-5y = -8
y = $\frac{8}{5}$

x + 2($\frac{8}{5}$) = 2
x + $\frac{16}{5}$ = 2
x = $- \frac{6}{5}$

The solution set is ($- \frac{6}{5}$, $\frac{8}{5}$)

Dec 28, 2015

$x = - 1.2 \text{ and } y = 1.6$

#### Explanation:

First, we need to isolate one variable - $x$ in this case:
$x + 2 y = 2$ becomes $x = 2 - 2 y$.
Then, we take this "new value" of x and put in the second equation:
$\left(2 - 2 y\right) - 3 y = - 6$ which becomes $y = \frac{8}{5} \text{ or } 1.6$ when solved.
Having this new value of $y$, we go back to the first equation and solve it, finding $x$ :
$x = 2 - \frac{16}{5} = \frac{10}{5} - \frac{16}{5} = - \frac{6}{5} \text{ or} - 1.2$