Question

Steps to solve this equation.

Answer 1

Solve the following system:
{9 y - 4 x = 28 | (equation 1)
{-4 x - y = -28 | (equation 2)

Subtract equation 1 from equation 2:
{-(4 x) + 9 y = 28 | (equation 1)
{0 x - 10 y = -56 | (equation 2)

Divide equation 2 by -2:
{-(4 x) + 9 y = 28 | (equation 1)
{0 x+5 y = 28 | (equation 2)

Divide equation 2 by 5:
{-(4 x) + 9 y = 28 | (equation 1)
{0 x+y = 28/5 | (equation 2)

Subtract 9 × (equation 2) from equation 1:
{-(4 x)+0 y = (-112)/5 | (equation 1)
{0 x+y = 28/5 | (equation 2)

Divide equation 1 by -4:
{x+0 y = 28/5 | (equation 1)
{0 x+y = 28/5 | (equation 2)

Collect results:
Answer:   {x = 28/5
                 {y = 28/5

Answer 2

-4x+9y=28
-4x-y=-28

Solve for one variable in either equation, then substitute it in the other equation to find the other variable.

-4x+9y=28
Add 4x to both sides
9y=28+4x
Divide both sides by 9
y=(28+4x) / 9

-4x-y=-28
-4x- ((28+4x) / 9)= -28
-4x-28/9-4x/9=-28
Multiply everything by -9 to get rid of denominators
(-9)(-4x)-(-9)(28/9)-(-9)(4x/9)=(-9)(-28)
36x+28+4x=252
40x+28=252
Subtract 28 from both sides
40x=224
Divide both sides by 40
x=5.6

Substitute x=5.6 back in to now solve for y.
-4x+9y=28
(-4)(5.6)+9y=28
-22.4+9y=28
Add -22.4 to both sides
9y=50.4
Divide both sides by 9
y=5.6

Hope this helps! :)