4a+6b=10
2a-4b=12

what does 12a =?

If you have at least as many equations as your have unknown variables, the 'system' is solvable (unless the equations are copies of eachother).

In this case, isolate one letter and plug it in the other. I'm going for the 2a in the bottom one (it doesn't matter)

2a - 4b = 12 => (divide by two and move the b's to the other side)

a = 6 + 2b. (plug this one into the top equation)

4(6+2b) + 6b = 10 => 24+8b+6b = 10 => 24 + 14b = 10 => 14b = -14 => b=-1

a = 6 + -2 = 4.

So a=4 and b=-1. 

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