Advanced Algebra: Example 3

In order to force a variable to cancel out, we must make one set of coefficients match—either both x terms or both y terms. We can do this by multiplying each equation by an appropriate number:

Now that our y terms have the same coefficient, we can add our equations. Note that we are adding in this case because our y coefficients, although equal in value, have opposite signs—one is positive and one is negative:

Since we know x, we can plug this value into our first equation to find y:

Since x + y = 10 + 2 = 12, Choice (E) is correct.