# How do you solve the following system?: 3x +11y =-4, -9x +5y = 2

Jan 26, 2016

$\left(x , y\right) = \left(- \frac{7}{19} , - \frac{5}{19}\right)$

#### Explanation:

Solve by elimination:-

$3 x + 11 y = - 4 , - 9 x + 5 y = 2$

It is possible to eliminate $- 9 x$ by $3 x$ if we multiply $3 x$ by $3$ to get $9 x$

$\rightarrow 3 \left(3 x + 11 y = - 4\right)$

$\rightarrow 9 x + 33 y = - 12$

Now add both of the equations:-

$\rightarrow \left(- 9 x + 5 y = 2\right) + \left(9 x + 33 y = - 12\right) = \left(38 y = - 10\right)$

$\rightarrow 38 y = - 10$

$\rightarrow y = - \frac{10}{38} = - \frac{5}{19}$

Now substitute the value of y to the first equation:-

$\rightarrow - 9 x + 5 \left(- \frac{5}{19}\right) = 2$

$\rightarrow - 9 x - \frac{25}{19} = 2$

$\rightarrow - 9 x = 2 + \frac{25}{19} = \frac{63}{19}$

$\rightarrow x = \frac{63}{19} \div \left(- 9\right) = \frac{63}{19} \cdot \left(- \frac{1}{9}\right) = - \frac{63}{171} = - \frac{7}{19}$

So,$\left(x , y\right) = \left(- \frac{7}{19} , - \frac{5}{19}\right)$