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Solving equations with two unknowns

Solving equations with two unknowns

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Tutor: Alice

Summary

Solving equations with two unknowns

​​In a nutshell

An equation with two unknowns is an equation with two variables that you do not know the value of. In some cases there may only be one solution, in others there may be a few and in many cases there could be infinite solutions!


Finding solutions to equations with two unknowns

Finding the solutions is all about using trial and error - trying out every possible solution.


Example 1

What are the possible whole number solutions to 2x+4y=162x + 4y = 162x+4y=16 ?

​xxx​​
​yyy​​
​2x+4y2x+4y2x+4y​​
​000​​
​444​​
​0+16=160+16=160+16=16​​
​222​​
​333​​
​4+12=164+12=164+12=16​​
​444​​
​222​​
​8+8=168+8=168+8=16​​
​666​​
​111​​
​12+4=1612+4=1612+4=16​​
​888​​
​000​​
​16+0=1616+0 = 1616+0=16​​

There are five pairs of solutions: (0,4),(2,3),(4,2),(6,1)‾\underline{(0,4) , (2,3) , (4,2) , (6,1)}(0,4),(2,3),(4,2),(6,1)​​ and (8,0)‾\underline{(8,0)}(8,0)​.


Using a table

The easiest way to test out all the solutions is by using a table.


Example 2

Alex has some 20p20p20p​ and 50p50p50p​ coins. He has £2.70£2.70£2.70​ all together. How many of each coin could he have?


Using a table:

​50p50p50p​​
​20p20p20p​​
​50x+20y=?50x+20y=?50x+20y=?​​
​111​​
111111​
​£2.70£2.70£2.70​​
​222​​
not possible
​​​
​333​​
666​
​£2.70£2.70£2.70​​
​444​​
not possible
​​​
​555​​
111​
​£2.70£2.70£2.70​​


There are three possible combinations of coin that Alex could have:

1×50p‾\underline{1\times50p}1×50p​​ and 11×20p‾\underline{11 \times 20p}11×20p​

​3×50p‾\underline{3\times50p}3×50p​ and 6×20p‾\underline{6\times20p}6×20p​​

5×50p‾\underline{5\times50p}5×50p​​ and 1×20p‾\underline{1\times20p}1×20p​​

​

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Formulae for the area and volume of shapes

Unit 1

Formulae for the area and volume of shapes

Simple formulae

Unit 2

Simple formulae

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Solving equations with two unknowns

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Solving equations with two unknowns

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FAQs - Frequently Asked Questions

How do I solve an equation with two unknowns?

The easiest way to test out all the solutions is by using a table. Use trial and error to test every possible solution until you have found them all.

Can an equation with two unknowns have more than one solution?

In some cases there may only be one solution, in others there may be a few and in many cases there could be infinite solutions!

What is an equation with two unknowns?

An equation with two unknowns is an equation with two variables that you do not know the value of.

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