# How do you solve 2x+9y=10 and x=4-4y?

May 21, 2016

The solution for the system of equations is:
color(green)(x = -4

color(green)(y=2

#### Explanation:

$2 x + 9 y = 10$.......equation $\left(1\right)$

color(blue)(x = 4-4y..............equation $\left(2\right)$

Solving by substitution:

Substituting equation $2$ into equation $1 :$

$2 x + 9 y = 10$

$2 \cdot \left(\textcolor{b l u e}{4 - 4 y}\right) + 9 y = 10$

$\textcolor{b l u e}{8 - 8 y} + 9 y = 10$

$8 + y = 10$

$y = 10 - 8$

color(green)(y=2

Finding $x$ from equation $2 :$

$x = 4 - 4 y$

$x = 4 - \left(4 \cdot 2\right)$

$x = 4 - 8$

color(green)(x = -4