# How do you solve the system 2x - 15y = 33 and -3x + 4y = - 5?

Jun 28, 2015

#### Answer:

$x = - \frac{171}{111}$ and $y = - \frac{89}{37}$

#### Explanation:

(1) $2 x - 15 y = 33$
(2) $- 3 x + 4 y = - 5$

Let's eliminate the $x$ variable.

Multiply Equation (1) by 3 and Equation (2) by 2. This gives

(3) $6 x - 45 y = 99$
(4) $- 6 x + 8 y = - 10$

Add Equations (3) and (4).

(5) $- 37 y = 89$

(6) $y = - \frac{89}{37}$

Substitute (6) in (2).

-3x+4y= -3x + 4(-89/37) = -3x – 356/37 = -5

$- 3 x = \frac{356}{37} - 5 = \frac{356 - 185}{37} = \frac{171}{37}$

$x = - \frac{171}{111}$

Check: Substitute in (2).

-3x +4y = -3(-171/111) +4(-89/37) = 513/111 -356/37 = (37×513-111× 356)/(111×37) = (18981-39516)/4107 = -20535/4107 = 5