# How do you solve the following system?:  2x +4y =-9 , 2x +y = -2

Mar 15, 2017

$\left(\frac{1}{6} , - \frac{7}{3}\right)$

#### Explanation:

Labelling the equations.

$\textcolor{red}{2 x} + 4 y = - 9 \to \left(1\right)$

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

Notice that the term $\textcolor{red}{2 x}$ is common to both equations.

Thus, subtracting (2) from (1) will eliminate it leaving an equation in y which we can solve.

$\text{Subtract "(1)-(2)" term by term}$

$\left(\textcolor{red}{2 x - 2 x}\right) + \left(4 y - y\right) = \left(- 9 - \left(- 2\right)\right)$

$\Rightarrow 3 y = -$7

divide both sides by 3

$\frac{\cancel{3} y}{\cancel{3}} = \frac{- 7}{3}$

$\Rightarrow y = - \frac{7}{3}$

Substitute this value into either (1) or (2) and solve for x

Substituting in ( 2)

$2 x - \frac{7}{3} = - 2$

$\Rightarrow 2 x = - 2 + \frac{7}{3} = \frac{1}{3}$

dividing both sides by 2

$\frac{\cancel{2} x}{\cancel{2}} = \frac{\frac{1}{3}}{2}$

$\Rightarrow x = \frac{1}{3} \times \frac{1}{2} = \frac{1}{6}$

$\Rightarrow \left(\frac{1}{6} , - \frac{7}{3}\right) \text{ is the solution}$
graph{(y+2x+2)(y+1/2x+9/4)=0 [-12.66, 12.65, -6.33, 6.33]}