How do solve the following linear system?: -4x + 9y = 9 , -3x + 7y= -16 4x+9y=9,3x+7y=16?

1 Answer
Apr 9, 2017

x = -207 x=207 and y = -91 y=91

Explanation:

We will solve this using substitution (although you can solve it with other methods, I prefer this one).

First, we must rewrite the two equations and make sure they have an identical term. I will rewrite them as follows:

-4x + 9y = 9 4x+9y=9 will become -12x + 27y = 27 12x+27y=27

-3x + 7y = -16 3x+7y=16 will become -12x + 28y = -64 12x+28y=64

Now as you can see, both equations now have -12x 12x in common. We will use this to substitute.

We will rewrite one equation, let's use the first one, to isolate -12x 12x.

-12x + 27y = 27 12x+27y=27 will become -12x = 27 - 27y 12x=2727y

Now we can substitute this into the second equation to find the first variable.

-12x + 28y = -64 12x+28y=64
(27 - 27y) + 28y = -64 (2727y)+28y=64
27 - 27y + 28y = -64 2727y+28y=64
27 + y = -64 27+y=64
y = -91 y=91

Now that we have found the value of y y, we can move on to substitute this value to find x x.

Take an original question, we'll use the first one, and substitute our y y value.

-4x + 9y = 9 4x+9y=9
-4x + 9 (-91) = 9 4x+9(91)=9
-4x - 819 = 9 4x819=9
-4x = 828 4x=828
x = -207 x=207

So now we have solved the two equations to get y = -91 y=91 and x = -207 x=207.