Simultaneous Equations (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.

This information can be used to write down two equations.
One of these is .

Write down the other equation.

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.

Use this information to write down two equations in and .

                                                                                  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.

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