# How do you solve the following system?: 13x +17y =11, -6x +5y = -27

Dec 10, 2017

Express y in terms of x and insert the expression in the other equation.

#### Explanation:

Substitution means expressing one variable in terms of another. So, you'll need to remake the expression in such a way that x (or y, doesn't matter) will be alone on one side of the equation.

Let's pick the second one for this, since it seems easier:
$- 6 x + 5 y = - 27$
$- 6 x = - 5 y - 27$
$x = \frac{5}{6} y + 4.5$

Then, insert the last expression in the other equation:
$13 x + 17 y = 11$
$13 \left(\frac{5}{6} y + 4.5\right) + 17 y = 11$
$\frac{65}{6} y + 58.5 + 17 y = 11$
$\frac{65}{6} y + \frac{102}{6} y = - 58.5 + 11$
$\frac{167}{6} y = - 47.5$
$\frac{167}{6} y = - \frac{285}{6}$
$167 y = - 285$
$y = - \frac{285}{167}$ which is around -1.7066.

Then, replace the found y in the equation with isolated x to find x:
$x = \frac{5}{6} \cdot \left(- \frac{285}{167}\right) + 4.5$
$x = 3.0778$

$x = 3.0778$
$y = - 1.7066$