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

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
${\displaystyle 3(6x-2y=8)\to 18x-6y=24}$
${\displaystyle -2(9x-3y=12)\to -18x+6y=-24}$
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
${\displaystyle y=\frac{6x-8}{2}}$
y=3x-4
Result: There are infinitely many solutions of the form y=3x-4, where x=any real number.