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

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:

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

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

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

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

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

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

$- 12 x + 28 y = - 64$
$\left(27 - 27 y\right) + 28 y = - 64$
$27 - 27 y + 28 y = - 64$
$27 + y = - 64$
$y = - 91$

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.

$- 4 x + 9 y = 9$
$- 4 x + 9 \left(- 91\right) = 9$
$- 4 x - 819 = 9$
$- 4 x = 828$
$x = - 207$

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