Simultaneous equations · Year 11

In Year 11 you learn: simultaneous equations from problems.

Simultaneous equations are two equations with two unknowns that are both true at the same time. Solving them finds the one pair of values that fits both — on a graph, it is the point where the two lines cross.

Key facts

• Elimination: make the coefficients of one letter match, then add the equations (if the signs differ) or subtract them (if the signs are the same).
• Substitution: rearrange one equation for one letter and substitute it into the other.
• Once you have one unknown, substitute back to find the other, then check in both equations.
• Graphically, the solution is where the two graphs intersect.
• With one linear and one quadratic equation, substitute the linear one into the quadratic; there can be 0, 1 or 2 solutions.

Worked examples

Other years

• Simultaneous equations · Year 9
• Simultaneous equations · Year 10
• Simultaneous equations · Year 12