If 2x + 3y = 26 and 7x – 5y = 60, then x + y =
2x + 3y = 26
7x – 5y = 60
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.
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