# How do you solve the following system: 3x-y=12, 4x-y=6 ?

Feb 24, 2016

I'll solve this systems of equations for you by substitution

#### Explanation:

We must first isolate a variable.

$3 x - y = 12$

$- y = 12 - 3 x$

$y = - 12 + 3 x$

Now, knowing y, we can substitute for y in the other equation.

$4 x - \left(- 12 + 3 x\right) = 6$

$4 x + 12 - 3 x = 6$

$x = - 6$

$3 \left(- 6\right) - y = 12$

$- 18 - y = 12$

$- y = 30$

$y = - 30$

The solution set is $\left\{- 6 , - 30\right\}$. Note that the solution set must always be of the form $\left\{x , y\right\}$, as noted in graphing. Eg. the point (8,5) is 8 on the x axis and 5 on the y axis graph.

Hopefully this helps!