4. Find (a) the x -intercept and (b) the y -intercept of each of the following linear equations and hence graph each line.
(i) x + 2y = 6 (ii) x − 2y = 10
(iii) − x + 3y = 12 (iv) 5x + 90 = 3y
5. Find (a) the x-intercept and (b) the y-intercept of each of the following linear equations and hence graph each line.
(i) x + y = 5 (ii) 3 x + 2y = 12
(iii) − 5x − 2y = 10 (iv) 10y − 30 = 3x
6. Solve the following simultaneous equations graphically.
(i) y − x = 1 and x + y = 3 (ii) y − x = 1 and x + y = 5 (iii) y = 6 − x and y = x + 4 (iv) x + y = 0 and 2x − y = 9
7. Solve the following simultaneous equations graphically and verify your answer in each equation.
(i) 2x − 3y = 4 and 3y − x = 4 (ii) x + 3y = 4 and 3x − y = 2 (iii) 5x − y = 2 and 2x + y = 5
8. Solve the following simultaneous equations graphically and verify your answer in each equation.
(i) x + y + 3 = 0 and x + 3y − 1 = 0 (ii) x = y + 6 and y = 2x − 3 (iii) x = y and x = − y (iv) x + y = 4 and 2x − y = 2
9. The path of a beam of light is described using the equation 5x − 3y = 26 . The path of a second beam of light is described using the equation 2x + y = 17 . Find the point at which the two beams of light meet.
10. The path of a rocket is described using the equation 3x + 2y = 36 A second rocket is fi red to intercept the fi rst. Its path is described using the equation 5x + 4y = 64
(i) Find the value for x and the value for y where these two rockets meet.
(ii) Every one unit on the y -axis = 100 metres. Find the maximum height reached by both rockets.
11. Copy the table below and put a tick (✓) in the correct box in each row to show whether each statement is always true, sometimes true, or never true. Justify your answer in each case.
Statement (i) Graphs of linear equations cross the x- axis
(ii) Two lines on the Cartesian plane cross at some point (iii) A graph of a linear equation can cross the x -axis more than once
Tick one box only for each statement Always true Sometimes true Never true