Question

How do you solve by substitution `4x-9y=-21` and `4x+3y=-9`?

Answer 1

`(A): 4x-9y=-21`
`(B): 4x+3y=-9`
We firstly obtain x or y from (A):
`4x=9y-21`

`x=9/4y-21/4`

And then we put this result at the place of x in (B).

`4(x)+3y=-9 -> 4(9/4y-21/4)+3y=-9`
`9y-21+3y=-9`
`12y=12`
`y=1`

It is not the end! Now that we found y we have to find x. We can basically substitute y=-5/2 in one of the two equations (for example `(A)` ).
`4x-9(y)=-21 -> 4x-9(1)=-21`
`4x=-21+9=-12`
`x=-3`

So the solution of the system is `(x,y)=(-3,1)`