How do you solve a dMAT Mathematical Equations question with letters as unknowns?

The trick is mental substitution: start with whichever equation gives you a direct value first, then substitute that value through the rest of the system. Every dMAT equation set has exactly one valid solution, so there is always a way in if you find the most constrained equation first.

Two Worked Examples

Take a system like 7 + A = 14 and B - 3 = A. Solving the first equation gives A = 7. Substituting A = 7 into the second equation gives B = 10. A harder-style example: if A = 2B, B + C = 9, and A - C = 3, substitute A = 2B into the third equation to get 2B - C = 3; combine this with B + C = 9 by adding the two equations together, which gives 3B = 12, so B = 4 and C = 9 - 4 = 5.

The Skill Being Tested

The skill throughout is mental substitution under time pressure, not advanced algebra. Start with whichever equation gives you a direct value first, then substitute that value through the rest of the system, since every dMAT equation set has exactly one valid solution and there is always a way in if you find the most constrained equation first.

My Advice

Before attempting to solve any equation set, spend two or three seconds scanning for the single most constrained equation, usually the one with the fewest unknowns or a direct numeric relationship. Starting there instead of the first equation on the page consistently saves time across a full 25-minute subtest.