Simultaneous Equations (Cambridge (CIE) IGCSE Maths: Core)

Solve the simultaneous equations. You must show all your working.

Solve the simultaneous equations.

You must show all your working.

The equations of two straight lines are and .

Use algebra to solve these two simultaneous equations to find the co-ordinates of the point where the lines meet.
You must show all your working.

A shop sells pens and notebooks. The cost of a pen is  cents and the cost of a notebook is  cents.

On Monday, the shop sells 5 pens and 4 notebooks for 450 cents.

Complete the equation.

..................

On Tuesday, the shop sells 10 pens and 3 notebooks for 525 cents.

Write this information as an equation.

................................................ = .........................

Solve your two equations to find the cost of a pen and the cost of a notebook.

You must show all your working.

Cost of a pen = ...................................... cents  Cost of a notebook = ...................................... cents 

Beindu goes to the market to buy apples and bananas.

She can buy

• 7 apples and 4 bananas for 85 cents

or

• 3 apples and 8 bananas for 93 cents.

Apples cost  cents each and bananas cost  cents each.

i) This information can be used to write down two equations. One of these is . Write down the other equation.

....................... = ............... [2]

ii) Solve these two simultaneous equations. You must show all your working.

a = .................................      

b = .................................  [3]

The Fraser family and the Singh family go to the cinema.
The Fraser family buys 6 adult tickets and 2 child tickets for $124. The Singh family buys 3 adult tickets and 5 child tickets for $100.

Find the price of an adult ticket and the price of a child ticket.

Adult ticket $ .....................................................

Child ticket $ .................................................

A plant costs dollars and a bush costs dollars.
Ana buys 2 plants and 4 bushes for $42.
Paola buys 7 plants and 9 bushes for $107.

Write down a pair of simultaneous equations and solve them to find the value of and the value of .
You must show all your working.

Alphonse is years old and Beatrice is  years old.

Three times Alphonse’s age is equal to 5 times Beatrice’s age. Twice Beatrice’s age is 4 years more than Alphonse’s age.

i) Use this information to write down two equations in and .

[2]

ii) Find the age of Alphonse and the age of Beatrice.

                                                                  Alphonse .................................. years old   

Beatrice .................................. years old [3]

Des thinks of two numbers.
The sum of his two numbers is -6.
The difference between his two numbers is 62.

Find the two numbers.

..................... and .....................

A cost to hire a minibus depends on the number of hours it is hired for, and the number of passengers.
The cost is $h per hour plus $p per passenger.

i) When the minibus is hired for 3 hours with 10 passengers the cost is $61.

Complete the equation.

............................

[1]

 ii) When the minibus is hired for 5 hours with 8 passengers the cost is $80.

Write this information as an equation.

[2]

iii) Solve your two simultaneous equations to find and . You must show all your working. 

................................................       

................................................[4]