Substituting into systems without the parentheses
y = 2x − 3 goes into 3x − 2y = 12, and without parentheses the −2 only hits the 2x.
Why it happens
Substitution is mentally 'replace a letter', but algebraically it's 'replace a letter with a wrapped expression'. Skipping the wrapper drops a distribution.
See the trap
y = 2x − 3 and 3x − 2y = 12. Find x.
✗ The trap: 3x − 2·2x − 3 = 12 → −x − 3 = 12 → x = −15.
✓ The fix: 3x − 2(2x − 3) = 12 → 3x − 4x + 6 = 12 → x = −6.
How to actually fix it
- Substitute with parentheses around the entire expression, always.
- Distribute in its own line before combining terms.
- Plug your solution into BOTH original equations to verify.
Made this mistake on a real question?
Practice Algebra questions here. Miss one and it is logged with the exact error, then brought back until you beat it.
Practice Algebra →FAQ
Is elimination safer than substitution?
It avoids this trap but has its own (sign errors when subtracting rows). Pick per problem: substitution when a variable is already isolated.
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.