 # Solving Simple Simultaneous Equations

In this worksheet, students solve simple simultaneous equations by eliminating one variable. Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Understand Expressions, Equations, Inequalities, Terms and Factors

Difficulty level:   ### QUESTION 1 of 10

Simultaneous equations involve two variables, each of whose value must be found.

The following method quickly eliminates one of the variables, so that the resulting equation can be solved normally.

Example 1

Solve simultaneously

x + y = 4

x - y = 2

x + y = 4     (a)

x - y = 2      (b)

We can eliminate y by adding (a) to (b)

This gives 2x = 6

So x = 3

Substitute this x value into one of the equations, say (a) to get

3 + y = 4

y= 1

Check by putting this into the other equation (b) to get 3 - 1 = 2

Solution is x = 3, y = 1

Example 2

Solve simultaneously

3x + y = 25

x + y = 11

3x + y = 25     (a)

x + y = 11      (b)

We can eliminate y by subtracting (b) from (a) to get

2x = 14

x = 7

Substitute this x value in say equation (b) to get 7 + y = 11

So y = 4

Check in equation (a) to get 3 x 7 + 4 = 21 + 4 = 25

Solution is x = 7, y = 4

Solve simultaneously:

x + y = 15

x - y = 9

x = 3, y = 12

x = 12, y = 3

x = 13, y = 2

Solve simultaneously:

x + y = 19

x - y = 15

x = 17, y = 12

x = 12, y = 3

x = 17, y = 2

Solve simultaneously:

x + y = 7

2x - y = 2

x = 4, y = 3

x = 3, y = 4

x = 4, y = 2

Solve simultaneously:

x + y = 6

3x - y = 10

x = 4, y = 2

x = 2, y = 4

x = 4, y = -2

Solve simultaneously:

x + y = 11

5x - y = 25

x = 5, y = 6

x = 5, y = 5

x = 6, y = 5

Solve simultaneously:

6x + y = 16

2x + y = 8

x = 2, y = 4

x = 3, y = 4

x = 6, y = 4

Solve simultaneously:

x + 8y = 26

x + y = 5

x = 3, y = 2

x = 2, y = 3

x = 18, y = 1

Solve simultaneously:

x + 7y = 28

x + 2y = 13

x = 3, y = 7

x = 7, y = 3

x = 21, y = 1

Solve simultaneously:

x + 5y = 11

x + 4y = 10

x = 3, y = 6

x = 6, y = 4

x = 6, y = 1

Solve simultaneously:

6x + y = 16

3x + y = 10

x = 2, y = 4

x = 1, y = 7

x = 1, y = 10

• Question 1

Solve simultaneously:

x + y = 15

x - y = 9

x = 12, y = 3
EDDIE SAYS
Add the equations to eliminate y 2x = 24 x = 12 Substitute this value of x into the first equation to find y x + y = 15 12 + y = 15 y = 3
• Question 2

Solve simultaneously:

x + y = 19

x - y = 15

x = 17, y = 2
EDDIE SAYS
Add the equations to eliminate y 2x = 34 x = 17 Substitute this value of x into the first equation to find y x + y = 19 17 + y = 19 y = 2
• Question 3

Solve simultaneously:

x + y = 7

2x - y = 2

x = 3, y = 4
EDDIE SAYS
Add the equations to eliminate y 3x = 9 x = 3 Substitute this value of x into the first equation to find y x + y = 7 3 + y = 7 y = 4
• Question 4

Solve simultaneously:

x + y = 6

3x - y = 10

x = 4, y = 2
EDDIE SAYS
Add the equations to eliminate y 4x = 16 x = 4 Substitute this value of x into the first equation to find y x + y = 6 4 + y = 6 y = 2
• Question 5

Solve simultaneously:

x + y = 11

5x - y = 25

x = 6, y = 5
EDDIE SAYS
Add the equations to eliminate y 6x = 36 x = 6 Substitute this value of x into the first equation to find y x + y = 11 6 + y = 11 y = 5
• Question 6

Solve simultaneously:

6x + y = 16

2x + y = 8

x = 2, y = 4
EDDIE SAYS
Subtract the equations to eliminate y 4x = 8 x = 2 Substitute this value of x into the first equation to find y 6x + y = 16 6(2) + y = 16 12 + y = 16 y = 4
• Question 7

Solve simultaneously:

x + 8y = 26

x + y = 5

x = 2, y = 3
EDDIE SAYS
Subtract the equations to eliminate y 7y = 21 y = 3 Substitute this value of y into the second equation to find x x + y = 5 x + 3 = 5 x = 2
• Question 8

Solve simultaneously:

x + 7y = 28

x + 2y = 13

x = 7, y = 3
EDDIE SAYS
Subtract the equations to eliminate x 5y = 15 y = 3 Substitute this value of y into the second equation to find x x + 2y = 13 x + 2(3) = 13 x + 6 = 13 x = 7
• Question 9

Solve simultaneously:

x + 5y = 11

x + 4y = 10

x = 6, y = 1
EDDIE SAYS
Subtract the equations to eliminate x y = 11 Substitute this value of y into the first equation to find x x + 5y = 11 x + 5(1) = 11 x+ 5 = 11 x=6
• Question 10

Solve simultaneously:

6x + y = 16

3x + y = 10

x = 2, y = 4
EDDIE SAYS
Subtract the equations to eliminate y 3x = 6 x = 2 Substitute this value of x into the second equation to find y 3x + y = 10 3(2) + y = 10 6 + y = 10 y = 4
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