# Solve the following system of equations. 6x-2y=8 9x-3y=12

Solve the following system of equations.
6x-2y=8
9x-3y=12
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Corben Pittman
Step 1
We will solve this by elimination. We will try to eliminate y.
We multiply the first equation by 3 and the second equation by -2
$3\left(6x-2y=8\right)\to 18x-6y=24$
$-2\left(9x-3y=12\right)\to -18x+6y=-24$
Step 2
Then if we add the two equations then we get
18x-6y=24
-18x+6y=-24
0=0
Which is always true.
So there are infinitely many solutions to the system of equations.
We solve y for x
6x-2y=8
2y=6x-8
$y=\frac{6x-8}{2}$
y=3x-4
Result: There are infinitely many solutions of the form y=3x-4, where x=any real number.
Jeffrey Jordon