How do solve the following linear system?: 5x + y = 9 , -4x + 9y = 9 ?

Apr 14, 2016

The solution for the system of equations is :
$x = \frac{72}{49}$

$y = \frac{81}{49}$

Explanation:

$5 x + y = 9$, multiplying by $9$
$45 x + \textcolor{b l u e}{9 y} = 81$...............equation $\left(1\right)$

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

Solving by elimination

Subtracting equation $2$ from $1$ :

$45 x + \cancel{\textcolor{b l u e}{9 y}} = 81$

$+ 4 x - \cancel{\textcolor{b l u e}{9 y}} = - 9$

$49 x = 72$

$x = \frac{72}{49}$

Finding $y$ from equation $1$
$45 x + 9 y = 81$

$9 y = 81 - 45 x$

$9 y = 81 - 45 \cdot \left(\frac{72}{49}\right)$

$9 y = \frac{3969}{49} - \left(\frac{3240}{49}\right)$

$9 y = \frac{729}{49}$

$y = \frac{729}{49 \cdot 9}$

$y = \frac{81}{49}$