Junior Secondary · Mathematics

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 questions24 marksFree, no account

Question 1

1 mark

If \(2x + y = 5\) and \(y = 3\), what is the value of \(x\)?

Question 2

1 mark

The perimeter of a rectangle is \(24\text{ cm}\). If its length is \(2\text{ cm}\) longer than its width, find the area of the rectangle.

Question 3

1 mark

The ratio of the price of a burger to a soda is \(5:2\). If a customer buys 2 burgers and 3 sodas, the total cost is \(\$64\). Find the price of one burger.

Question 4

1 mark

Solve the following simultaneous linear equations for \(y\):
\(x + 4y = 18\)
\(x - y = 3\)

Question 5

1 mark

A shop sells strawberries in large boxes and small boxes. 2 large boxes and 5 small boxes contain a total of 80 strawberries. 3 large boxes and 2 small boxes contain a total of 65 strawberries. How many strawberries are in each large box?

Question 6

2 marks

Solve the following system of linear equations for \(x\) and \(y\):
\(y = 3x\)
\(x + y = 12\)

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

Question 7

4 marks

Solve the following system of linear equations for \(x\) and \(y\):
\(\frac{x}{3} + \frac{y}{2} = 5\)
\(x - y = 5\)

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Question 8

5 marks

Solve the following system of equations for \(x\) and \(y\):

\( \frac{1}{x} + \frac{1}{y} = \frac{5}{6} \)

\( \frac{3}{x} - \frac{2}{y} = \frac{1}{6} \)

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

Question 9

3 marks

A delivery truck carries two types of packages: Type A and Type B. It is known that:

2 packages of Type A and 5 packages of Type B weigh a total of \(24\) kg.
2 packages of Type A and 3 packages of Type B weigh a total of \(16\) kg.

(a) Let \(x\) kg be the weight of a Type A package and \(y\) kg be the weight of a Type B package. Form a pair of simultaneous linear equations to represent the information above.
(b) By solving the equations in (a), find the weight of one Type A package and one Type B package.

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Question 10

5 marks

In a farm, there are some chickens and rabbits. Let the number of chickens be \(x\) and the number of rabbits be \(y\). It is known that:

(i) The total number of animals is 35.
(ii) The total number of legs is 94.

(a) Form a pair of simultaneous linear equations in \(x\) and \(y\) to represent the above information.
(b) Solve the simultaneous equations to find the number of chickens and the number of rabbits in the farm.
(c) If a new rabbit is added to the farm, find the new ratio of the number of chickens to the number of rabbits.

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

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