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Simultaneous Equations Mock Assessment
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Simultaneous Equations Mock Assessment
Answer every question. Show clear working for written solutions. For multiple-choice questions, select one answer.
Part A: Multiple Choice
Choose the best answer for each question.
1.Find the ordered pair that satisfies both equations: 2x + y = 11 and x − y = 1.
- (x, y) = (3, 5)
- (x, y) = (4, 3)
- (x, y) = (5, 1)
- (x, y) = (2, 7)
2.Which method is most direct for solving the system 5x + 2y = 19 and y = 3?
- Substitution
- Elimination
- Completing the square
- Differentiation
3.The graphs of two distinct parallel straight lines represent a simultaneous system with:
- Exactly one solution
- No solution
- Infinitely many solutions
- Exactly two solutions
Part B: Solve and Apply
Show your working for each question.
4.Use elimination to solve the system 3x + 2y = 16 and 2x − 2y = 4.
5.Use substitution to solve y = 3x + 2 and 2x + y = 17.
6.At a market, 3 jars of honey and 2 loaves of bread cost $31. Two jars of honey and 3 loaves of bread cost $29. Find the price of one jar of honey and one loaf of bread.
7.Two numbers have a sum of 34 and a difference of 10. Find the two numbers.
Part C: Graphs and Further Reasoning
Use algebra and graphical reasoning where appropriate.
8.Find the intersection of y = 2x − 1 and y = −x + 5 by solving the equations algebraically. Then sketch both lines in the space below and mark their intersection.
Use this space to sketch and label both straight lines.
9.Write a pair of linear equations whose solution is x = −1 and y = 4.
10.Find a and b so that the system 3x + 2y = 8 and ax + by = 20 has infinitely many solutions.
3 printable pages
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