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

Mar 15, 2017

$\left(7 , 5\right)$

#### Explanation:

Labelling the equation.

$x \textcolor{red}{+ y} = 12 \to \left(1\right)$

$x \textcolor{red}{- y} = 2 \to \left(2\right)$

Note that adding + y and - y will eliminate them and leave an equation we can solve.

$\text{Adding "(1)+(2)"term by term gives}$

$\left(x + x\right) + \left(\textcolor{red}{+ y - y}\right) = \left(12 + 2\right)$

$\Rightarrow 2 x = 14$

divide both sides by 2

$\Rightarrow x = 7$

Substitute this value into either of the 2 equation, to find the corresponding value of y

$\text{Substituting in } \left(1\right)$

$7 + y = 12 \Rightarrow y = 12 - 7$

$\Rightarrow y = 5$

$\textcolor{b l u e}{\text{As a check}}$

Substitute these values into both equations and if both sides are equal then they are the solution.

$\text{left side of "(1)to7+5=12to"true}$

$\text{left side of "(2)to7-5=2to"true}$

$\Rightarrow \left(7 , 5\right) \text{ is the solution}$
graph{(y+x-12)(y-x+2)=0 [-11.1, 11.09, -5.55, 5.55]}