# How do you solve 3x + 7y = 18 and x + 2y = 5?

Jun 14, 2016

The solution for the system of equations is:

color(green)(x=-1

color(green)(y = 3

#### Explanation:

$3 x + 7 y = 18$........equation $\left(1\right)$

$x + 2 y = 5$
color(blue)(x = 5 - 2y .............equation $\left(2\right)$

Substituting equation $2$ in equation $1 :$

$3 x + 7 y = 18$

$3 \times \left(\textcolor{b l u e}{5 - 2 y}\right) + 7 y = 18$

$15 - 6 y + 7 y = 18$

$15 + y = 18$

$y = 18 - 15$

color(green)(y = 3

Now we substitute the value of $y$ in equation $2$ to find $x :$

color(blue)(x = 5 - 2y

$x = 5 - 2 \times \left(3\right)$

$x = 5 - 6$

color(green)(x=-1