SAT systems of equations: line up the variable before you add
Two equations, and the question wants only y. Substitution will get there; elimination gets there in one line — if the signs survive.
Why it happens
Adding two equations is safe. Subtracting means distributing a minus sign across every term on both sides, and the term that gets forgotten is almost always the constant on the right. The result still looks like a reasonable answer, so nothing warns you.
See the trap
2x + 5y = 31 and 6x − 4y = 17. Find y.
Multiplying the first by 3 and subtracting, but negating only the left-hand side.
6x + 15y = 93. Subtract the second: 19y = 76, so y = 4 — the minus applied to 17 as well.
How to actually fix it
- 1Scale one equation so a variable's coefficients match in size.
- 2If the matching signs are opposite, add — it is safer, and no distribution is needed.
- 3If you must subtract, write the negated equation out in full on its own line before combining.
Practice this trap · 7 real questions
Each of these is a question from the free bank that turns on the mistake above — the trap is the reason its wrong answer looks right. Easiest first.
FAQ
How do I know whether to eliminate x or y?
Eliminate the one the question does not ask for. If it asks for y, remove x — otherwise you solve the whole system and then have to substitute back, which is where the extra step goes wrong.
How do I stop repeating this mistake?
Reading the explanation isn't enough — your brain needs to beat the trap on a fresh question. Practice the skill in the kaoshen.co question bank: miss one and it is logged with the exact error, then brought back to you three days later and again after fourteen.
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