# How do you solve the system 5x + 3y =3 and x+ 9y = 2?

Jun 2, 2015

$5 x + 3 y = 3$......equation$\left(1\right)$
$x + 9 y = 2$
x=color(blue)( 2-9y .........equation $\left(2\right)$

Solving by substitution
substituting equation $\left(2\right)$ in equation $\left(1\right)$

$5 x + 3 y = 3$
$5 \textcolor{b l u e}{\left(2 - 9 y\right)} + 3 y = 3$
$10 - 45 y + 3 y = 3$
$- 42 y = - 7$
$\textcolor{b l u e}{y} = \frac{1}{6}$

finding the value of $x$ by substituting the value of $y$ in equation $\left(2\right)$
$x = 2 - 9 y$
$x = 2 - 9 \left(\frac{1}{6}\right)$
$\textcolor{b l u e}{x} = \frac{12 - 9}{6} = \frac{3}{6} = \frac{1}{2}$

the solution for the system of equations is
color(blue)( x = 1/2 , y =1/6