Revision sheet

Linear equations

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

Watch out: distribute to every term.

Solving for a variable

Same moves as with numbers; the other letters are just numbers you do not know.

Watch out: divide every term.

Lines from equations

Intercepts: set the other variable to 0. Slope: solve for $y$.

Watch out: slope of $Ax + By = C$ is $-A/B$.

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.

How many solutions?

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

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

Inequalities

Solve as an equation; flip when multiplying or dividing by a negative.

Watch out: check with a number from your answer.

Absolute value equations and inequalities

|x − a| = b: a ± b. Less than: between. Greater than: outside.

Watch out: do not forget the negative case.

Inequalities in two variables

Dashed for $<, >$; solid for $\le, \ge$. Test a point to choose the side.

Watch out: “at most” is $\le$, “at least” is $\ge$.