Pure · Algebra & functions
Chapter 1 · 4
The idea
Simultaneous equations and inequalities
Solving two equations at once (including a line meeting a curve), and solving linear and quadratic inequalities — including the sign-flip and the inside/outside rule for quadratics.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Pure · Algebra & functions
Simultaneous equations and inequalities
Solving two equations at once (including a line meeting a curve), and solving linear and quadratic inequalities — including the sign-flip and the inside/outside rule for quadratics.
Why it works
Where two graphs cross
Simultaneous equations ask for the values that satisfy both statements at once — graphically, where the two graphs cross. For two linear equations, eliminate one variable (add or subtract the equations so a variable cancels) or substitute one into the other. Two straight lines meet at one point, so expect one pair.A line meeting a curve
For one linear and one quadratic, rearrange the linear equation for one variable and substitute it into the other. You'll land on a single quadratic; solve it, then substitute each back to get its partner . A line can cut a curve in up to two places, so expect up to two pairs — and always quote them as pairs, not a loose list of numbers.Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
Start freeTakes a minute — no card.