# Rearranging Equations

In this worksheet, students rearrange equations so that they are in the form ax + by = c.

Key stage:  KS 4

Curriculum topic:  Algebra

Difficulty level:

### QUESTION 1 of 10

In this worksheet, you must rearrange equations so that they are in the form

ax + by = c

where:

a ≥ 0

a and b cannot both be 0

a and b are integers

the HCF of a, b, and c is 1

Example

Rearrange the following equation so that it is in the form ax + bx = c

2y = 4x - 12

We use the standard rule of all equations,

DO THE SAME TO BOTH SIDES

2y = 4x - 12

Subtract 4x from both sides, so that the letters are on the left, to get:

2y - 4x = -12

Multiply both sides by -1 so that the coefficient of x is positive, to get:

4x - 2y = 12

Divide by the HCF = 2, to get:

2x - y = 6

Rearrange the following equation so that it is in the form ax + bx = c,

where a ≥ 0, a and b cannot both be 0, a and b are integers and the HCF of a, b, and c is 1.

2y = 4x - 8

2x - y = 4

4x - 2y = 8

y - 2x = 4

Rearrange the following equation so that it is in the form ax + bx = c,

where a ≥ 0, a and b cannot both be 0, a and b are integers and the HCF of a, b, and c is 1.

y = 4x - 8

2x - y = 4

4x - y = 8

y - 4x = -8

Rearrange the following equation so that it is in the form ax + bx = c,

where a ≥ 0, a and b cannot both be 0, a and b are integers and the HCF of a, b, and c is 1.

y = 8 - 4x

4x + y = 8

4x - y = 8

y - 4x = -8

Rearrange the following equation so that it is in the form ax + bx = c,

where a ≥ 0, a and b cannot both be 0, a and b are integers and the HCF of a, b, and c is 1.

3y = 9 - 6x

2x + y = 3

3x - 2y = 9

2x + y = 9

Rearrange the following equation so that it is in the form ax + bx = c,

where a ≥ 0, a and b cannot both be 0, a and b are integers and the HCF of a, b, and c is 1.

6y = 9 - 6x

2x + y = 9

3x - 2y = 9

2x + 2y = 3

Rearrange the following equation so that it is in the form ax + bx = c,

where a ≥ 0, a and b cannot both be 0, a and b are integers and the HCF of a, b, and c is 1.

½y = 9 - 6x

12x + y = 9

12x + y = 18

2x + 2y = 3

Rearrange the following equation so that it is in the form ax + bx = c,

where a ≥ 0, a and b cannot both be 0, a and b are integers and the HCF of a, b, and c is 1.

½y = -4 - 2x

4x + y = -8

4x + y = 8

4x + 2y = -8

Rearrange the following equation so that it is in the form ax + bx = c,

where a ≥ 0, a and b cannot both be 0, a and b are integers and the HCF of a, b, and c is 1.

½y = -2 - ½x

2x + y = -4

4x + y = 4

x + y = -4

Rearrange the following equation so that it is in the form ax + bx = c,

where a ≥ 0, a and b cannot both be 0, a and b are integers and the HCF of a, b, and c is 1.

¼y = 4 - 2½x

10x + y = 16

5x + 2y = 8

2½x + ¼y = 4

Rearrange the following equation so that it is in the form ax + bx = c,

where a ≥ 0, a and b cannot both be 0, a and b are integers and the HCF of a, b, and c is 1.

4¾y = 4 - 2¼x

2x + 4y = 19

9x + 19y = 16

2¼x + 4¾y = 4

• Question 1

Rearrange the following equation so that it is in the form ax + bx = c,

where a ≥ 0, a and b cannot both be 0, a and b are integers and the HCF of a, b, and c is 1.

2y = 4x - 8

2x - y = 4
EDDIE SAYS
2y - 4x = -8
4x - 2y = 8
2x - y = 4
• Question 2

Rearrange the following equation so that it is in the form ax + bx = c,

where a ≥ 0, a and b cannot both be 0, a and b are integers and the HCF of a, b, and c is 1.

y = 4x - 8

4x - y = 8
EDDIE SAYS
4x - 8 = y
4x - y = 8
• Question 3

Rearrange the following equation so that it is in the form ax + bx = c,

where a ≥ 0, a and b cannot both be 0, a and b are integers and the HCF of a, b, and c is 1.

y = 8 - 4x

4x + y = 8
EDDIE SAYS
y + 4x = 8
4x + y = 8
• Question 4

Rearrange the following equation so that it is in the form ax + bx = c,

where a ≥ 0, a and b cannot both be 0, a and b are integers and the HCF of a, b, and c is 1.

3y = 9 - 6x

2x + y = 3
EDDIE SAYS
3y = 9 - 6x
6x + 3y = 9
2x + y = 3
• Question 5

Rearrange the following equation so that it is in the form ax + bx = c,

where a ≥ 0, a and b cannot both be 0, a and b are integers and the HCF of a, b, and c is 1.

6y = 9 - 6x

2x + 2y = 3
EDDIE SAYS
6y = 9 - 6x
6x + 6y = 9
2x + 2y = 3
• Question 6

Rearrange the following equation so that it is in the form ax + bx = c,

where a ≥ 0, a and b cannot both be 0, a and b are integers and the HCF of a, b, and c is 1.

½y = 9 - 6x

12x + y = 18
EDDIE SAYS
½y = 9 - 6x
6x + ½y = 9
12x + y = 18
• Question 7

Rearrange the following equation so that it is in the form ax + bx = c,

where a ≥ 0, a and b cannot both be 0, a and b are integers and the HCF of a, b, and c is 1.

½y = -4 - 2x

4x + y = -8
EDDIE SAYS
½y = -4 - 2x
2x + ½y = -4
4x + y = -8
• Question 8

Rearrange the following equation so that it is in the form ax + bx = c,

where a ≥ 0, a and b cannot both be 0, a and b are integers and the HCF of a, b, and c is 1.

½y = -2 - ½x

x + y = -4
EDDIE SAYS
½y = -2 - ½x
½x + ½y = -2
x + y = -4
• Question 9

Rearrange the following equation so that it is in the form ax + bx = c,

where a ≥ 0, a and b cannot both be 0, a and b are integers and the HCF of a, b, and c is 1.

¼y = 4 - 2½x

10x + y = 16
EDDIE SAYS
¼y = 4 - 2½x
2½x + ¼y = 4
Multiply by 4 to get:
10x + y = 16
• Question 10

Rearrange the following equation so that it is in the form ax + bx = c,

where a ≥ 0, a and b cannot both be 0, a and b are integers and the HCF of a, b, and c is 1.

4¾y = 4 - 2¼x

9x + 19y = 16
EDDIE SAYS
4¾y = 4 - 2¼x
2¼x + 4¾y = 4
Multiply by 4 to get:
9x + 19y = 16
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