# Manipulating systems of equations

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## Lesson details

### Key learning points

- In this lesson, we will manipulate systems of equations in order to eliminate an unknown. We will look at cases where one equation can be altered to enable elimination by addition or subtraction.

### Licence

This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.

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### 5 Questions

Q1.

3x+2y=5 AND 3x-2y=7. If I add these two equations together, which unknown will be eliminated?

both

neither

x

Q2.

3x+2y=5 AND 3x-2y=7. If I subtract the two equations, which unknown will be eliminated?

both

neither

y

Q3.

3x-5y=17 AND 2x-5y=10. Subtract the first equation from the second equation.

5x=27

x-10y=7

y=7

Q4.

2x-5y=10 AND 3x-5y=17. Add the two equations together.

10y=27

5x=27

Q5.

3x-5y=17 AND 7x-5y=20. How can I eliminate y from these simultaneous equations?

add

you can't eliminate y

### 5 Questions

Q1.

x+y=6. Multiply this equation by 3.

3x+3y=6

3x+y=6

x+y=18

Q2.

x+y=3 AND 2x-y=5 This pair of equations has been transformed. Which of the following are equivalent to the original pair?

2x+2y=6 AND 2x+y=5

6x+y=9 AND 10x-5y=25

x+y=7 AND 2x-y=9

Q3.

x+y=3 AND 2x-y=5 This pair of equations has been transformed. Which of the following are equivalent to the original pair?

Option 1

Option 3

Option 4

Q4.

2x+5y=9 AND 5x+4y=14. Solve the simultaneous equations.

x=2

y=3 and x=-2

Q5.

10x+5y=5 AND 3x-5y=34. Solve the simultaneous equations.

x=1 and y = -1

x=3