How can I solve a system of two equations, like $A + B = 13$ and $2D + B = 13$?

Question

I am currently studying for my SSAT and this question appeared in my practice book:

When $A + B = 13$ and $2D + B = 13$, what is the value of $D$?

(A) 13

(B) 5

(C) -5

(D) -7

(E) It cannot be determined from the information given

How can I go about solving this and other questions that are similar in the future?

Answer 1

Here's a solution that uses nothing more than basic algebra. The basic idea is to solve everything in terms of $D$ and see if this limits the values of $D$.

If we solve the second equation for $B$ we get $$B=13-2D$$

Solving the first equation for $A$ then substituting our expression for $B$ we get $$A=13-B=13-(13-2D)=2D$$

We can easily check that these expressions solve the two equations.

This shows that $D$ could have any values and we could still find solutions to the equations. Therefore, we cannot determine the value of $D$ from the information given, and the correct answer to the problem is (E).