Pearson Edexcel IGCSE · Mathematics (Specification A)

Simultaneous linear equations: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Simultaneous linear equations.

10 questions27 marksFree, no account

Question 1

1 mark

Solve the following simultaneous linear equations:
\(x + y = 15\)
\(x - y = 3\)

Question 2

1 mark

Solve the following simultaneous linear equations:
\(2x + 3y = 13\)
\(5x - y = 7\)
Find the value of \(x + y\).

Question 3

1 mark

Two lines have equations \(y = ax + b\) and \(y = bx + a\).
They intersect at the point \((2, 5)\).

Work out the values of \(a\) and \(b\).

Question 4

1 mark

A rectangular field has a perimeter of \(40\) m. The length of the field is \(4\) m more than its width.

Find the dimensions of the field and determine its area.

Question 5

1 mark

Solve the following simultaneous linear equations to find the values of \(x\) and \(y\):

\(\frac{x}{2} + \frac{y}{3} = 7\)

\(\frac{x}{4} - \frac{y}{2} = -1\)

Question 6

4 marks

Solve the simultaneous linear equations:
\(5x + 2y = 11\)
\(4x - 3y = 18\)

Write your answer out first, then check it against the worked solution.

Question 7

6 marks

The lines with equations \(y = ax + b\) and \(y = bx + a\) intersect at the point \((2, 5)\).
Work out the values of \(a\) and \(b\) by setting up and solving simultaneous linear equations.

Write your answer out first, then check it against the worked solution.

Question 8

4 marks

Find the exact solution of the following simultaneous linear equations:
\(4x + 3y = 2\)
\(3x + 5y = -15\)

Write your answer out first, then check it against the worked solution.

Question 9

3 marks

Solve the following simultaneous linear equations:
\(x + y = 14\)
\(x - y = 2\)

Find the values of \(x\) and \(y\).

Write your answer out first, then check it against the worked solution.

Question 10

5 marks

At a cafe, 3 coffees and 2 teas cost \(\pounds 10.80\).
5 coffees and 4 teas cost \(\pounds 19.20\).

(a) Write down a pair of simultaneous linear equations to represent this information.

(b) Solve your equations to find the cost of one coffee and the cost of one tea.

Write your answer out first, then check it against the worked solution.

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