# How do you solve the system of equations -16x - 4y = 12 and - 4x + y = - 11?

Oct 6, 2016

$x = 1 \mathmr{and} y = - 7$

#### Explanation:

Given 2 equations, let us number them

$- 16 x - 4 y = 12$
we can simplify this equation by 4 , it would be easier for solving

$\Rightarrow \frac{- 16 x - 4 y}{4} = \frac{12}{4}$
rArrcolor(blue)(-4x-y=3 equation1

the two equations are:

$\textcolor{b l u e}{- 4 x - y = 3}$
$\textcolor{red}{- 4 x + y = - 11}$

First we add both equations :
$\textcolor{b l u e}{- 4 x - y} \textcolor{red}{- 4 x + y} = 3 - 11$
$- 8 x + 0 y = - 8$
$- 8 x = - 8$
$x = - \frac{8}{-} 8$
$\textcolor{g r e e n}{x = 1}$

second, let us substitute the value of $x$ in equation 2
$\textcolor{red}{- 4 \cdot 1 + y = - 11}$
$\Rightarrow - 4 + y = - 11$
$\Rightarrow y = - 11 + 4$
$\textcolor{g r e e n}{y = - 7}$

Third, check if the values color(green)(x=1 and color(green)(y=-7) by substituting it in equation 1
$\textcolor{b l u e}{- 4 x - y = 3}$
color(blue)(-4(color(green)1)-(color(green)(-7))=?3)
color(blue)(-4+7=?3)
-3=?-3 true

therefore,x=1 and y=-7#