IMAT 2015 Q55 [Satisfaction]

The variables x and y satisfy the following two equations:

x + 3y = 13
2x – y = 5

What is the value of x + y ?

A. 7
B. 8
C. 6
D. 9
E. 10

The fastest way to do this, without thinking too much is to express one valuable as a function of the other.

From the first equation, we can express x= 13-3y
Using that, we will change the x in the second equation to the expression from the first one: 2x-y=5 \to 2(13-3y) - y=5
\to 26 - 6y - y =5 \to -7y = 5-26 \to -7y = -21 \to y = \frac{-21}{-7}
\to y = \frac{21}{7} =3

Having that information, we can find how much x+y is putting the value that we got for y, and the expressed x.

x+y = 13-3y+y = 13-2y = 13-2 \cdot 3= 13-6 = 7

So the answer to this question is (A) x+y=7