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

1 Answer
Apr 9, 2017

x = -207 and 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 will become -12x + 27y = 27

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

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

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

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

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

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

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

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

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

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