Question

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

Answer 1

`x = 7/19 and y = -20/19`

Explanation:

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

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

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

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

Bx2: `" "6x+4y=-2`........................................................D

C+D:`" " 19y= -20`

`y = (-20)/19`

Substitute `(-20)/19` for y in B

`3x + 2((-20)/19) = -1 " "xx19`

`19xx3x + (-40)/19xx19 = -1xx19`

`57x-40 = -19`

`57x = 21`

`x = 21/57 = 7/19`

Check in A

`(-2xx7)/19 +(5xx(-20))/19`

`(-14-100)/19`

`-114/19`

=`-6`