# How do you solve the following system?:  -2x +5y =-6 , 3x +2y = -1

Aug 15, 2016

$x = \frac{7}{19} \mathmr{and} y = - \frac{20}{19}$

#### Explanation:

As the x-terms have different signs, we will eliminate them by using an LCM of 6 and adding.

$- 2 x + 5 y = - 6$.............................................. A

$3 x + 2 y = - 1$....................................................B

Ax3: $- 6 x + 15 y = - 18$.......... ......................................C

Bx2: $\text{ } 6 x + 4 y = - 2$........................................................D

C+D:$\text{ } 19 y = - 20$

$y = \frac{- 20}{19}$

Substitute $\frac{- 20}{19}$ for y in B

$3 x + 2 \left(\frac{- 20}{19}\right) = - 1 \text{ } \times 19$

$19 \times 3 x + \frac{- 40}{19} \times 19 = - 1 \times 19$

$57 x - 40 = - 19$

$57 x = 21$

$x = \frac{21}{57} = \frac{7}{19}$

Check in A

$\frac{- 2 \times 7}{19} + \frac{5 \times \left(- 20\right)}{19}$

$\frac{- 14 - 100}{19}$

$- \frac{114}{19}$

=$- 6$