Step One:

We can multiply the top equation by 3 and the multiply the bottom equation by -1.

Step Two:

When we multiply the top by 3 and the bottom by -1 we get

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these new equations. Now, we can cancel out the 6x and the -6x, the 3y and -3y, and even the 12 and the -12.

Step Three:

When we cancel out the variables, and the constants, we get the solution 0 = 0. This means that there are infinitely many solutions. There is no need to plug this back into either of the original equations.

Step Four:

Since we get 0 = 0, our solution is infinitely many solutions.

Answer: Infinitely many solutions

Double-Check

If you were to graph the two equations, you would see that the two lines are parallel! They will never touch. Furthermore, if you were to change them into slope-intercept form, they would have the same slope.