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Linear equations

Do the same to both sides until $x$ is alone.

Watch out: distribute to every term.

How many solutions?

$3 = 7$ : none. $5 = 5$ : all. $x =$ a number: one.

Watch out: a true statement like $2 = 2$ means infinitely many.

How many solutions?

Different slopes: one. Parallel: none. Same line: infinitely many.

Watch out: same slope alone is not enough; check the intercepts.

Substitution

Replace one variable by its expression, solve, then substitute back.

Watch out: answer the variable the question asks for.

Elimination

Equal coefficients: subtract. Opposite coefficients: add.

Watch out: multiply first when no coefficients match.

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