# How do you solve the following system?: 4x-y=-1 , 6x - 4y = 3

May 25, 2018

Use the elimination method.

x = $- \frac{7}{10}$
y = $\frac{9}{5}$

#### Explanation:

I'd say for this one, I would use the elimination method. I'm not too good at formatting, but I'll give this my best shot.
Set it up like this:
4x - y = -1
6x - 4y= 3
Now, you want to get rid of one of the variables. Multiply (4x-y=-1) by -4. Now you have:
-16x + 4y = 4
6x - 4y = 3
Cancel out the 4y and -4y and add the rest of the similar terms. You're left with
-10x = 7
Divide both sides by -10 so you have just x.
x = $- \frac{7}{10}$

Now, plug x back into one of the equations. You can do either, but for this one I'll do the first one.
4( $- \frac{7}{10}$) - y = -1
4($- \frac{7}{10}$)= $- \frac{28}{10} = - \frac{14}{5}$
So...
$- \frac{14}{5}$ - y = -1
Move the $\frac{14}{5}$ to the other side in order to isolate the y, by adding it.
-y = $- \frac{9}{5}$
Divide both sides by -1.
y = $\frac{9}{5}$

x = $- \frac{7}{10}$
y = $\frac{9}{5}$