# How do you solve -x + y = 12 and x + 2y = 3?

Aug 1, 2015

$\left\{\begin{matrix}x = - 7 \\ y = 5\end{matrix}\right.$

#### Explanation:

All you really ahve to do to solve this system of equations is add the left side and the right side of the equations separately to eliminate the variable $x$.

$- \textcolor{red}{\cancel{\textcolor{b l a c k}{x}}} + y + \textcolor{red}{\cancel{\textcolor{b l a c k}{x}}} + 2 y = 12 + 3$

$3 y = 15$

To get the value of $y$, simply divide both sides of the equation by $2$ to get

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} \cdot y}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} = \frac{15}{3} \implies y = \textcolor{g r e e n}{5}$

Now use this value of $y$ in one of the two equations to get the value of $x$.

$x + 2 \cdot 5 = 3$

$x + 10 = 3$

Add $- 10$ to both sides of the equation

$x + \textcolor{red}{\cancel{\textcolor{b l a c k}{10}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{10}}} = 3 - 10 \implies y = \textcolor{g r e e n}{- 7}$

Aug 1, 2015

I found:
$x = - 7$
$y = 5$

#### Explanation:

You can add the two equations (in column):
{-x+y=12
{x+2y=3
$\textcolor{red}{0 + 3 y = 15}$
so $y = \frac{15}{3} = 5$
substitute this value into the first equatiom:
$- x + 5 = 12$
$- x = 7$
$x = - 7$