Solving two linear equations by elimination and substitution, forming them from word problems, and solving a linear equation together with a quadratic.
5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
Two unknowns, two clues. Pens and books, adult and child tickets, two lines crossing — simultaneous equations find the one answer that fits both clues.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
The solution is where two lines cross.
Copy these into your notebook in your own words — that is how they stick.
Make the coefficients of one letter equal in size; add if opposite signs, subtract if same signs.
Rearrange one equation to y = … or x = …, substitute into the other.
Substitute the solution into BOTH original equations.
The solution is the intersection of the two lines.
Define both letters, write two equations, solve, answer in words with units.
Substitute the linear equation into the quadratic → solve a quadratic → find both pairs.
Linear–linear: one (or none/infinitely many for parallel/same lines). Linear–quadratic: 0, 1 or 2 pairs.
Always write each solution as an (x, y) pair so x and y stay together.
3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Mathematics Arcade.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (19 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [11 marks]
Answer all parts.
(a) Solve algebraically: 4x + 3y = 17 and 2x − y = 1. [3]
(b) Two adult tickets and three child tickets cost $44. One adult ticket and two child tickets cost $26. Form two equations and find the price of an adult ticket and of a child ticket. [4]
(c) Solve the simultaneous equations y = 2x + 1 and y = x² − 2. [4]
Question 2 [8 marks]
A shop sells notebooks (n dollars each) and pens (p dollars each). 4 notebooks and 3 pens cost $27. 2 notebooks and 5 pens cost $24.
(a) Write two equations in n and p. [2]
(b) Solve the equations to find the price of a notebook and a pen. [4]
(c) Hence find the cost of 3 notebooks and 2 pens. [2]
Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.