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  1. Maths
  2. Year 9
  3. Algebra: Equations
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Solve Simultaneous Equations by Eliminating One Variable

In this worksheet, students solve simultaneous equations by eliminating one variable.

'Solve Simultaneous Equations by Eliminating One Variable' worksheet

Key stage:  KS 3

Curriculum topic:   Algebra

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

Difficulty level:  

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Worksheet Overview

QUESTION 1 of 10

In this worksheet, you must try to eliminate one of the letters to solve the simultaneous equations.

 

Example 1   
2x + 3y  = 21 - equation (1)
4x - 3y  = 15 - equation (2)
6x  = 36 adding (1) and (2)
   

 

x = 36 ÷ 6 = 6
   

 

Method

First look for the same number of x's or y's in both equations, in this case 3y.

If they have different signs, we add the two equations and are left with just x's.

If they have the same signs, as in the next example, we subtract to leave just one variable.

When we know one value, in this case x = 6, we substitute in one equation to find the other.

 
In equation (1)
 2 × 6 + 3y  = 21  
3y  = 9  
y  = 3  
   

 

We can check the answer by substituting both values in the other equation:

4 × 6 - 3 × 3 = 24 - 9 = 15 correct.

SOLUTION: x = 6 and y = 3

 
Example 2
7x - 4y  = 27 - (1)
4x - 4y  = 12 - (2)
3x  = 15 subtracting (1) and (2)
    x = 5
   

Substituting in (1)

7 × 5 - 4y = 27

35 - 4y = 27

- 4y = -8

y = 2


Checking in (2) 4 × 5 - 4 × 2 = 20 - 8 = 12 correct.

SOLUTION: x = 5 and y = 2
 

Solve the following equations simultaneously for x & y.

-7x + 4y = 20
-7x + 5y = 11
x =
 
y =
 

Column A

Column B

x
-9
y
-8

Solve the following equations simultaneously for x & y.

-2x - 2y = 32
-3x - 2y = 35
x =
 
y =
 

Column A

Column B

x
-13
y
-3

Solve the following simultaneous equations for x & y.

8x - 11y = 29
9x - 11y = 34
x =
 
y =
 

Column A

Column B

x
1
y
5

Solve the following equations simultaneously for x & y.

3x + 6y = 21
-10x + 6y = 34
x =
 
y =
 

Column A

Column B

x
-1
y
4

Solve the following simultaneous equations for x & y.

-11x - 8y = 11
-11x + 8y = 11
x =
 
y =
 

Column A

Column B

x
-1
y
0

Solve the following simultaneous equations for x & y.

-11x + 11y = 44
-11x + 10y = 36
x =
 
y =
 

Column A

Column B

x
4
y
8

Solve the following equations simultaneously for x & y.

-7x + 3y = 46
-8x + 3y = 47
x =
 
y =
 

Column A

Column B

x
-1
y
13

Solve the following simultaneous equations for x & y.

-9x + 5y = 9
2x + 5y = 53
x =
 
y =
 

Column A

Column B

x
9
y
4

Solve the following equations simultaneously for x & y.

7x - 6y = 33
7x - 4y = 43
x =
 
y =
 

Column A

Column B

x
5
y
9

Solve the following simultaneous equations for x & y.

-3x - 8y = 31
-11x - 8y = 7
x =
 
y =
 

Column A

Column B

x
3
y
-5
  • ANSWERS
  • Question 1

Solve the following equations simultaneously for x & y.

-7x + 4y = 20
-7x + 5y = 11
x =
 
y =
 
CORRECT ANSWER

Column A

Column B

x
-8
y
-9
  • ANSWERS
  • Question 2

Solve the following equations simultaneously for x & y.

-2x - 2y = 32
-3x - 2y = 35
x =
 
y =
 
CORRECT ANSWER

Column A

Column B

x
-3
y
-13
  • ANSWERS
  • Question 3

Solve the following simultaneous equations for x & y.

8x - 11y = 29
9x - 11y = 34
x =
 
y =
 
CORRECT ANSWER

Column A

Column B

x
5
y
1
  • ANSWERS
  • Question 4

Solve the following equations simultaneously for x & y.

3x + 6y = 21
-10x + 6y = 34
x =
 
y =
 
CORRECT ANSWER

Column A

Column B

x
-1
y
4
  • ANSWERS
  • Question 5

Solve the following simultaneous equations for x & y.

-11x - 8y = 11
-11x + 8y = 11
x =
 
y =
 
CORRECT ANSWER

Column A

Column B

x
-1
y
0
  • ANSWERS
  • Question 6

Solve the following simultaneous equations for x & y.

-11x + 11y = 44
-11x + 10y = 36
x =
 
y =
 
CORRECT ANSWER

Column A

Column B

x
4
y
8
  • ANSWERS
  • Question 7

Solve the following equations simultaneously for x & y.

-7x + 3y = 46
-8x + 3y = 47
x =
 
y =
 
CORRECT ANSWER

Column A

Column B

x
-1
y
13
  • ANSWERS
  • Question 8

Solve the following simultaneous equations for x & y.

-9x + 5y = 9
2x + 5y = 53
x =
 
y =
 
CORRECT ANSWER

Column A

Column B

x
4
y
9
  • ANSWERS
  • Question 9

Solve the following equations simultaneously for x & y.

7x - 6y = 33
7x - 4y = 43
x =
 
y =
 
CORRECT ANSWER

Column A

Column B

x
9
y
5
  • ANSWERS
  • Question 10

Solve the following simultaneous equations for x & y.

-3x - 8y = 31
-11x - 8y = 7
x =
 
y =
 
CORRECT ANSWER

Column A

Column B

x
3
y
-5
---- OR ----

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