Help solve this algebra 2 problem!?

Question

solve the system:
5x+9y=-6
4y=2-3x

Answer 1

Given equations are 5x + 9y = -6 and 4y = 2 - 3x

                               => 5x + 9((2 - 3x)/4) = -6     [ Since y = (2 - 3x)/4 ]

                               => 5x + (18 - 27x)/4 + 6 = 0

                               => 20x + 18 -27x + 24 = 0

                               => -7x + 42 = 0

                               => x = -42/-7

                               => x = 6

Substitute x value in 4y = 2 - 3x we get, 

                       => 4y = 2 - 3(6)

                       => 4y = 2 - 18

                        => 4y = -16

                        => y = -16/4 = -4

Therefore x = 6 and y = -4.

 

 

Answer 2

Given equations are

Multiply equation 1 with 3 and equation 2 with 5

Add multiplied equations 1 and 2

7y +28 = 0

Therefore 7y = -28 ==> y = -28/7==> y = -4

Substitute y = -4 in equation 2

3x + 4(-4) -2 =0===>3x - 16 - 2 = 0

= 3x -18 = 0==>3x = 18==> x = 18/3 ==>x = 6

Therefore the solutions for the given equation 1 and 2 is x = 6 and y = -4