The pair x + y = 7 with x − y = 1 has solution (4, 3), and 2x + y = 10 with x + y = 7 gives (3, 4), so this Year 9 sheet opens with two eliminations. The answers add (2, 5) and (3, 2) for later pairs.
Key Takeaways
x + y = 7 and x − y = 1 give x = 4, y = 3 (Q1).
2x + y = 10 and x + y = 7 give x = 3, y = 4 (Q2).
Q3 records (2, 5) as a pair solution.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.Solve the pair x + y = 7 and x - y = 1.
(a) x = 4, y = 3(b) x = 3, y = 4(c) x = 4, y = 1(d) x = 8, y = 7
2.Solve the pair 2x + y = 10 and x + y = 7.
(a) x = 3, y = 4(b) x = 4, y = 3(c) x = 3, y = 7(d) x = 7, y = 3
3.Find the point of intersection of y = 2x + 1 and y = x + 3.
(a) (2, 5)(b) (3, 5)(c) (2, 3)(d) (1, 3)
4.Solve the pair 3x + y = 11 and 2x - y = 4.
(a) x = 2, y = 3(b) x = 3, y = 2(c) x = 3, y = 11(d) x = 15, y = 4
5.Two numbers add to 12 and their difference is 4. What are the numbers?
(a) 6 and 6(b) 4 and 8(c) 5 and 7(d) 3 and 9
6.Solve the pair y = 3x and x + y = 8.
(a) x = 6, y = 2(b) x = 2, y = 6(c) x = 2, y = 3(d) x = 8, y = 3
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Solve x + y = 9 and x - y = 3.
8.Solve 2x + y = 7 and x + y = 4.
9.Solve y = 4x and x + y = 15.
10.Solve 2x - y = 5 and x + y = 7.
11.The lines y = 2x - 1 and y = x + 2 intersect at which point?
12.Solve 3x + 2y = 13 and x - 2y = -1.
13.Solve 5x - y = 13 and 2x + y = 8.
14.Two numbers sum to 10 and differ by 2. Find them.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.Two numbers add to 20 and differ by 6. Find the two numbers.
16.Two apples and one banana cost 90 cents. One apple and one banana cost 55 cents. Find the cost of one apple.
17.The sum of a mother's age and her daughter's age is 48. The mother is 30 years older. Find the daughter's age.
18.A pen costs p dollars and a pencil costs q dollars. If 3p + 2q = 13 and p + 2q = 7, find the cost of a pen.
19.The perimeter of a rectangle is 28 cm and its length is 6 cm more than its width. Find the width.
20.At a fair, 5 games cost the same as 3 rides. A ride costs 4 dollars more than a game. Find the cost of a ride.
Answer Key
1. a) x = 4, y = 3
2. a) x = 3, y = 4
3. a) (2, 5)
4. b) x = 3, y = 2
5. b) 4 and 8
6. b) x = 2, y = 6
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What solves x + y = 7 and x − y = 1?
x = 4, y = 3, option (a) in this worksheet (Q1).
What solves 2x + y = 10 and x + y = 7?
x = 3, y = 4, option (a) in this worksheet (Q2).
What is the intersection of the two lines?
The point (2, 5), option (a) in this worksheet (Q3).
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