# How do you solve the following system: 6x+2y=-4, -x+y=5?

Mar 12, 2016

$6 \cdot x + 2 \cdot y = - 4$
$- x + y = 5$
multiply 2nd by 2, gives.
$- 2 \cdot x + 2 \cdot y = 10$
subtract from top.
$8 \cdot x = - 14$
$x = - \frac{14}{8} = - 1.75$
$1.75 + y = 5$
$y = 5 - 1.75 = 3.25$
check $6 \cdot - 1.75 + 2 \cdot 3.25 = - 4$

Apr 1, 2016

$\left(x , y\right) = \left(- \frac{7}{4} , \frac{13}{4}\right)$

#### Explanation:

Solve by elimination and substitution

color(blue)(6x+2y=-4

color(blue)(-x+y=5

Multiply the second equation by $- 2$

$\rightarrow - 2 \left(- x + y = 5\right)$

$\rightarrow 2 x - 2 y = - 10$

Now,eliminate $2 y$ in the first equation by $- 2 y$ in the second equation

$\rightarrow \left(6 x + 2 y = - 4\right) + \left(2 x - 2 y = - 10\right)$

$\rightarrow 8 x = - 14$

color(green)(rArrx=-14/8=-7/4

Now,substitute the value of $x$ to the second equation

$\rightarrow - \left(- \frac{7}{4}\right) + y = 5$

$\rightarrow \frac{7}{4} + y = 5$

color(green)(rArry=5-7/4=13/4