Question 24316
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You say you are ending up with an equation that says something like "0=52".<br>
You are probably doing the algebra correctly; now you just need to learn what that result means.<br>
As you say, "0=52" is not true; that equation has no solutions.  Assuming you did the algebra correctly, that means the original pair of equations has no solution.<br>
When you are first learning algebra, it is important that you recognize this kind of result and understand what it means.<br>
An experienced student can look at this pair of equations and see that the "9x+6y" in the first equation is just 3 times the "3x+2y" in the second equation.  If you see that, then you can multiply the second equation by 3, making the pair of equations<br>
9x+6y=14
9x+6y=-33<br>
The expressions on the left are identical, so the expressions on the right should be identical.  Since they are not, the system of equations has no solution.<br>