Two equations, two unknowns
Use elimination (make one variable match, then add or subtract) or substitution (make one variable the subject and put it into the other equation).
Linear + quadratic: substitute, then solve a quadratic
Rearrange the linear equation and substitute into the quadratic to get a single quadratic in one variable; solve it, then find the matching values of the other variable.
Pair the answers correctly
A linear + quadratic pair usually has two solution points; each goes with its own — keep the pairs together.
Drawn from real examiner reports.
Trying to "square" the linear equation
Squaring to get is wrong (the right side of is not ); substitute instead.
Quadratic-formula denominator error
Writing the denominator as 2 instead of when the leading coefficient is not 1.
Only finding one variable
Solving for (or ) and stopping, without back-substituting to find its partner.
Substitute both solutions back into both equations
Each pair must satisfy both original equations — a fast, complete check.
Elimination: make one variable match, then add or subtract to remove it.
Substitution: make one variable the subject and put it into the other equation. Useful when a variable already has coefficient 1.
Two methods for linear simultaneous equations?
Solve the simultaneous equations You must show clear algebraic working.
