How do you solve the following system?: 4x-3y=15 , -6x+3y=17

Jan 30, 2016

$\left(x , y\right) = \left(- 16 , - \frac{79}{3}\right)$

Explanation:

Solve by elimination

$4 x - 3 y = 15$

$- 6 x + 3 y = 17$

If we loo carefully we can see that we can eliminate $3 y$ in the second equation by $- 3 y$ in the first equation.

$\rightarrow \left(4 x - 3 y = 15\right) + \left(- 6 x + 3 y = 17\right)$

$\rightarrow - 2 x = 32$

$\rightarrow x = \frac{32}{-} 2 = - 16$

So,substitute the value of $x$ to the first equation:

$\rightarrow 4 \left(- 16\right) - 3 y = 15$

$\rightarrow - 64 - 3 y = 15$

$\rightarrow - 3 y = 15 + 64$

$\rightarrow - 3 y = 79$

$\rightarrow y = - \frac{79}{3}$

So, $x = - 16 , y = - \frac{79}{3}$