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.

3x − 2·2x − 3 = 12 → −x − 3 = 12 → x = −15.

3x − 2(2x − 3) = 12 → 3x − 4x + 6 = 12 → x = −6.

How to actually fix it

1Substitute with parentheses around the entire expression, always.
2Distribute in its own line before combining terms.
3Plug your solution into BOTH original equations to verify.

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.

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