Simultaneous Equations — Year 9 Practice Questions
Work through these Year 9 practice questions on simultaneous equations. Try each one before revealing the worked solution.
Questions
Solve x + y = 10 and x − y = 4 by elimination.
Solve x + y = 8 and 2x + y = 11.
Solve y = 3x and x + y = 12 by substitution.
Solve 2x + y = 7 and y = x + 1.
Solve 3x + 2y = 16 and 3x − 2y = 8.
Solve 2x + 3y = 13 and 2x + y = 7.
Two numbers add up to 20 and differ by 6. Find the two numbers.
3 apples and 2 bananas cost $1.30; 1 apple and 2 bananas cost $0.90. Find the cost of one apple.
Answers & Worked Solutions
Question 1 Solution
Step 1: Add the equations: 2x = 14, so x = 7.
Step 2: Substitute: 7 + y = 10, so y = 3.
Answer: x = 7, y = 3
Question 2 Solution
Step 1: Subtract the first from the second: x = 3.
Step 2: Substitute: 3 + y = 8, so y = 5.
Answer: x = 3, y = 5
Question 3 Solution
Step 1: Substitute y = 3x: x + 3x = 12, so 4x = 12, x = 3.
Step 2: Then y = 3 × 3 = 9.
Answer: x = 3, y = 9
Question 4 Solution
Step 1: Substitute y = x + 1: 2x + x + 1 = 7, so 3x = 6, x = 2.
Step 2: Then y = 2 + 1 = 3.
Answer: x = 2, y = 3
Question 5 Solution
Step 1: Add the equations to eliminate y: 6x = 24, so x = 4.
Step 2: Substitute x = 4 into 3x + 2y = 16: 12 + 2y = 16, so y = 2.
Answer: x = 4, y = 2
Question 6 Solution
Step 1: Subtract the second from the first: 2y = 6, so y = 3.
Step 2: Substitute: 2x + 3 = 7, so 2x = 4, x = 2.
Answer: x = 2, y = 3
Question 7 Solution
Step 1: Let the numbers be x and y: x + y = 20 and x − y = 6.
Step 2: Add: 2x = 26, so x = 13; then y = 7.
Answer: 13 and 7
Question 8 Solution
Step 1: Form equations: 3a + 2b = 1.30 and a + 2b = 0.90.
Step 2: Subtract: 2a = 0.40, so a = $0.20.
Answer: $0.20
Build strong foundations in Simultaneous Equations
A free trial class with Teacher Rig helps your Year 9 child master Simultaneous Equations now — so IGCSE Maths feels familiar, not frightening, later.
Heading toward IGCSE? See how Simultaneous Equations develops in IGCSE Algebra and Graphs (Cambridge 0580) →