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Simultaneous Linear Equations Worksheet
Simultaneous Linear Equations
Long Questions Worksheet (Substitution • Elimination • Word Problems)
Instructions: Solve the following simultaneous linear equations. Show all working clearly.
Question 1
Consider the equations:
2x + y = 11
x − y = 1
a) Solve the equations using the substitution method.
b) Verify your solution in both equations.
c) Find the value of 3x + 2y.
Question 2
Solve the simultaneous equations:
3x + 2y = 16
2x − y = 1
a) Solve using the elimination method.
b) Find the value of x − y.
c) State whether the solution is unique.
Question 3
Given:
x + y = 7
2x + 3y = 17
a) Solve the equations.
b) Find the value of xy.
c) Hence calculate x² + y².
Question 4
Two numbers have a sum of 20 and a difference of 4.
a) Form two simultaneous equations.
b) Solve the equations.
c) Find the product of the two numbers.
Question 5
The perimeter of a rectangle is 52 cm. The length is 6 cm more than the width.
a) Form two equations using l and w.
b) Solve the equations.
c) Find the area of the rectangle.
Question 6
Solve the equations:
4x + y = 19
2x + y = 11
a) Solve using elimination.
b) Find x + y.
c) Find the value of 2x − y.
Question 7
Tickets for a show cost ₹120 for adults and ₹80 for children. The total cost of 10 tickets is ₹960.
a) Let a = number of adult tickets and c = number of child tickets. Form equations.
b) Solve the equations.
c) How many adult tickets were sold?
Question 8
Solve:
5x − 2y = 4
3x + y = 11
a) Solve the equations.
b) Find the value of x + y.
c) Find the value of 2x + 3y.
Question 9
The sum of two numbers is 30 and their difference is 6.
a) Form simultaneous equations.
b) Solve the equations.
c) Find the larger number.
Question 10
Solve the equations:
7x + 3y = 31
2x + y = 9
a) Solve the equations.
b) Find the value of x − y.
c) Verify the solution.
📘 View Complete Solutions
Q1: x = 4, y = 3; 3x + 2y = 18
Q2: x = 3, y = 4; x − y = −1; unique solution
Q3: x = 4, y = 3; xy = 12; x² + y² = 25
Q4: Numbers are 12 and 8; product = 96
Q5: Width = 10 cm, Length = 16 cm; Area = 160 cm²
Q6: x = 4, y = 3; x + y = 7; 2x − y = 5
Q7: Adults = 6, Children = 4
Q8: x = 3, y = 2; x + y = 5; 2x + 3y = 12
Q9: Numbers are 18 and 12; larger number = 18
Q10: x = 4, y = 1; x − y = 3