GCSEMathsEdexcelFoundationExam QuestionsAlgebraSimultaneous Equations

Simultaneous Equations (Edexcel GCSE Maths: Foundation): Exam Questions

Exam code: 1MA1

48 mins18 questions
Easy
Medium
Hard
1
Sme Calculator2 marks

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

2 x plus 5 y equals 34 2 x minus 3 y equals 2

x space equals space.......................... y space equals space..........................

How did you do?

2
Sme Calculator2 marks

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

table attributes columnalign right center left columnspacing 0px end attributes row cell 6 x plus 2 y end cell equals 4 row cell negative 6 x plus 3 y end cell equals 21 end table

 

x space equals space.......................... y space equals space..........................

How did you do?

3
Sme Calculator2 marks

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

9 x minus 5 y equals 28 4 x minus 5 y equals 18

 

x space equals space.......................... y space equals space..........................

How did you do?

4
Sme Calculator2 marks

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

table row cell 6 x minus 3 y space end cell equals 12 row cell 2 x space plus space 3 y space end cell equals 16 end table

x space equals ................................. 
y space equals .................................

How did you do?

5
Sme Calculator2 marks

Use substitution to solve the simultaneous equations.
You must show all your working.

table row cell 3 x plus 8 y end cell equals 28 row x equals cell 2 y end cell end table

 

x space equals space.......................... y space equals space..........................

How did you do?

1
Sme Calculator3 marks

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

table row cell x plus 3 y end cell equals 19 row cell negative 2 x plus 4 y end cell equals 32 end table

x space equals space...................................... space y space equals space...................................... space

How did you do?

2
Sme Calculator3 marks

Use substitution to solve the simultaneous equations.
You must show all your working.

table row cell 2 x minus 5 y end cell equals 32 row y equals cell 14 minus 3 x end cell end table

 

x space equals space.......................... y space equals space..........................

How did you do?

31 mark
A graph showing two straight lines that intersect, one with the equation y=x+1 and the other with the equation 4x+2y=8

Use the graphs to solve the simultaneous equations

table row cell 4 x plus 2 y end cell equals 8 row y equals cell x plus 1 end cell end table

  

x space equals space.......................... y space equals space..........................

How did you do?

4
Sme Calculator3 marks

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

table row cell 3 x minus 8 y end cell equals 22 row cell x plus 4 y end cell equals 4 end table

x space equals space...................................... space y space equals space...................................... space

How did you do?

5
Sme Calculator3 marks

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

                  table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x minus y end cell equals 22 row cell x plus 2 y end cell equals 5 end table

x space equals space................................................... space y space equals space................................................... space

How did you do?

6
Sme Calculator3 marks

Solve the simultaneous equations.

You must show all your working.

5 x minus 2 y space equals space 26 7 x plus 6 y space equals space 10

x equals............................ 

y equals............................ 

How did you do?

1
Sme Calculator3 marks

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

table attributes columnalign right center left columnspacing 0px end attributes row cell 5 x minus 9 y end cell equals 44 row cell 11 x plus 3 y end cell equals 17 end table

x space equals space...................................... space y space equals space...................................... space

How did you do?

2
Sme Calculator3 marks

Use substitution to solve the simultaneous equations.
You must show all your working. 

table row cell 4 x minus 7 y end cell equals 15 row cell 2 x end cell equals cell 3 y plus 6 end cell end table

 

x space equals space.......................... y space equals space..........................

How did you do?

31 mark
Graph showing two intersecting straight lines, one with equation x-y=-2 and the other with equation 4x+3y=12

Use the graphs to solve the simultaneous equations

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 x plus 3 y end cell equals 12 row cell x minus y end cell equals cell negative 2 end cell end table

  

x space equals space.......................... y space equals space..........................

How did you do?

4
Sme Calculator4 marks

Solve the simultaneous equations.

You must show all your working.

table attributes columnalign right center left columnspacing 0px end attributes row cell 5 x plus 4 y end cell equals 10 row cell 7 x minus 6 y end cell equals 43 end table

x space equals space................................................... space y space equals space................................................... space

How did you do?

5
Sme Calculator4 marks

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

table row cell 5 x minus 2 y end cell equals 44 row cell 2 x plus 3 y end cell equals 10 end table

table attributes columnalign right center left columnspacing 0px end attributes row cell x space end cell equals cell space................................................. space end cell row cell y space end cell equals cell space................................................. space end cell end table

How did you do?

6
Sme Calculator3 marks

The equations of two straight lines are y equals 3 x plus 13 and y equals 7 x minus 3.

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.

How did you do?

74 marks

A sweet shop sells two different types of sweets, Apple sours (a grams) and Bonbons (b grams).

3 apple sours and 4 bonbons are put on some scales and they are balanced with a block weighing 37 grams.

2 apple sours are put on some scales and they are balanced with 3 bonbons and a block weighing 2 grams.

Two lever balances with weights: left shows 3a & 4b balanced by 37; right shows 2a on one side, 3b & 2 on the other. Balances appear level.

Use the weight scales to calculate the mass in grams of each type of sweet purchased.

How did you do?