# How do you solve the system 7x-3y=19 , 5x+2y=-11?

Apr 17, 2016

$x = \frac{5}{29}$ and $y = - 5 \frac{27}{29}$

#### Explanation:

The two equations are

$7 x - 3 y = 19$ ............(A) and

$5 x + 2 y = - 11$ ...........(B)

Now multiplying (A) by $2$ and (B) by $3$, we get

$14 x - 6 y = 38$ ............(C) and

$15 x + 6 y = - 33$ ...........(D)

Adding (c) and (D), we get

$29 x = 5$ or $x = \frac{5}{29}$. Now putting this in (B)

$\frac{5 \times 5}{29} + 2 y = - 11$ or $\frac{25}{29} + 2 y = - 11$ or

$2 y = - \frac{25}{29} - 11 = - \frac{25}{29} - \frac{11 \times 29}{29} = \frac{- 25 - 319}{29} = - \frac{344}{29}$

$y = - \frac{344}{29} \times \frac{1}{2} = - \frac{172}{29} = = \frac{5 X X 29 + 27}{29} = - 5 \frac{27}{29}$