IGCSE Mathematics Worksheet- Simultaneous Equations

 

Answer the following

1.      Solve  3x + 4y = 14
            4x + 5y = 17

2.      Solve  3x + 2y = 7
            2x - 5y = 11

3.      Solve for x:   373x + 627y = 2492
                      627x + 373y = 3508

4.      Two numbers have a sum of 45 and a difference of 13. Find the numbers.

5.      John and Jacob each book in at the Sleepwell Lodge.
a) John stays for 3 nights and has breakfast on 2 mornings.
His bill is £145
Write down an algebraic equation to illustrate this.
b) Jacob stays for 5 nights and has breakfast on 3 mornings.
Her bill is £240.
Write down an equation to illustrate this.
c) Find the cost of one breakfast. 

6.      4 peaches and 3 grapefruit cost £1.30
Write down an algebraic equation to illustrate this.
b) 2 peaches and 4 grapefruit cost £1.20.
Write down an algebraic equation to illustrate this.
c) Find the cost of 3 peaches and 2 grapefruit. 

7.      A child has built a tower made of two types of brick.
It has three cylinders and two cuboids.
The total height of his tower is 38 centimetres.
Let x cm be the height of one cylinder and
let y be the height of one cuboid.
a) Construct an equation connecting x and y
He then built this second tower using two cylinders and five
cuboids, and its height was 51 centimetres.
b) Form a second equation in x and y and calculate the height
of both a cylinder and a cuboid.

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