# How do you solve the following system: 2x-5y=-19, y + 4x = 16 ?

Apr 23, 2016

$x = 3 \frac{17}{22}$ and $y = 4 \frac{10}{11}$

#### Explanation:

Putting value of $y$ from $y + 4 x = 16$ i.e. $y = 16 - 4 x$ in $2 x - 5 y = - 19$, we get

$2 x - 5 \left(16 - 4 x\right) = - 19$ or

$2 x - 80 + 20 x = - 19$ or

$22 x = 80 - 19 = 61$ or $x = \frac{61}{22} = 3 \frac{17}{22}$

Now putting this in $y = 16 - 4 x$ we get $y = 16 - \frac{4 \times 61}{22}$ or

$y = 16 - \frac{244}{22} = 16 - 11 \frac{2}{22} = 4 \frac{20}{22} = 4 \frac{10}{11}$