How do you solve by substitution 4x-9y=-214x−9y=−21 and 4x+3y=-94x+3y=−9?

1 Answer
Luca F.
Jun 8, 2015

(A): 4x-9y=-21(A):4x−9y=−21
(B): 4x+3y=-9(B):4x+3y=−9
We firstly obtain x or y from (A):
4x=9y-214x=9y−21

x=9/4y-21/4x=94y−214

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

4(x)+3y=-9 -> 4(9/4y-21/4)+3y=-94(x)+3y=−9→4(94y−214)+3y=−9
9y-21+3y=-99y−21+3y=−9
12y=1212y=12
y=1y=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)(A) ).
4x-9(y)=-21 -> 4x-9(1)=-214x−9(y)=−21→4x−9(1)=−21
4x=-21+9=-124x=−21+9=−12
x=-3x=−3

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

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