# How do you solve 5x+2y=12 and -6x-2y=-14?

Jan 21, 2016

$\left\{\begin{matrix}x = 2 \\ y = 1\end{matrix}\right.$

#### Explanation:

$\left\{\begin{matrix}5 x + 2 y = 12 \text{ S1" \\ -6x-2y=-14" S2}\end{matrix}\right.$

Looking at the equation we can see that in $S 1$ we have $a y$ and in $S 2$ we have $- a y$, thus we could use the Linear Systems with Addition or Subtraction to transform the system as :

$\left\{\begin{matrix}S 1 \\ S 1 + S 2\end{matrix}\right.$

$\left\{\begin{matrix}5 x + 2 y = 12 \\ - x + 0 y = - 2\end{matrix}\right. \implies \left\{\begin{matrix}5 x + 2 y = 12 \\ x = 2\end{matrix}\right.$

Now you can put the $x$ value in $S 1$ to find the $y$ value

$\left\{\begin{matrix}5 \cdot 2 + 2 y = 12 \\ x = 2\end{matrix}\right. \implies \left\{\begin{matrix}10 + 2 y = 12 \\ x = 2\end{matrix}\right. \implies \left\{\begin{matrix}5 x + 2 y = 12 \\ x = 2\end{matrix}\right.$

$\implies \left\{\begin{matrix}2 y = 12 - 10 \\ x = 2\end{matrix}\right. \implies \left\{\begin{matrix}y = {\cancel{2}}^{1} / {\cancel{2}}^{1} \\ x = 2\end{matrix}\right.$

$\implies \left\{\begin{matrix}x = 2 \\ y = 1\end{matrix}\right.$

graph{(5x+2y-12)(-6x-2y+14)=0 [-1.413, 5.518, -1.016, 2.45]}