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Linear Equations and Inequalities
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Linear Equations and Inequalities
Show your working where appropriate. Give monetary answers in dollars.
Linear Relationships
1.A shuttle service charges a fixed booking fee of $4.20 and $1.80 for each kilometre travelled. Which rule gives the total fare F for a trip of k kilometres?
- F = 1.80k + 4.20
- F = 4.20k + 1.80
- F = 1.80 + 4.20
- F = 4.20k
Hours booked
Total charge ($)
1
92
2
131
3
170
4
209
2.Using the community hall hire table, find the increase in charge for each extra hour and the fixed charge. State both amounts in dollars.
3.Select every linear relationship.
- y = 4x - 9
- y = x² + 1
- 3x + 2y = 10
- y = -6
Solving Equations and Inequalities
4.Solve 5x - 7 = 28.
5.A learner earns 3 marks for each correct answer and has already earned 12 bonus marks. They need at least 60 marks altogether to reach their target. Write an inequality for the number n of correct answers needed.
6.Solve 4x + 3 < 19. Show the solution on the number line.
Simultaneous Equations
7.Two internet plans have monthly costs given by P = 18 + 0.12g and Q = 30 + 0.06g, where g is the number of gigabytes used. Find the data use at which the costs are equal.
8.Solve the simultaneous equations: x + y = 9 and 2x - y = 6.
9.For the equations x + y = 9 and 2x - y = 6, explain what their solution (5, 4) represents when each equation is drawn as a straight line on the same coordinate plane.
2 printable pages
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