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### Solve algebraically: 6a + b = 16 5a - 2b = 19

We have two algebraic equations and we are trying to find what a and b can equal to fit for both situations.

1. 6a + b = 16

2. 5a - 2b = 19

The easiest method is substitution because we can sub in an equation for b by rearranging it.

therefore: b= 16 - 6a

From there on we can sub in b= 16 - 6a into equation 2. to give us:

5a - 2(16-6a) = 19

we expand the bracket to give:

5a - 32 +12a =19 **BE CAREFUL OF SIGNS**

17a -32 =19

17a = 51

therfore a = 3

We can use a=3 to sub back into equation 1

6(3) + b = 16

18 + b = 16

b= - 2

To check the two values for a and b are correct sub them back into equation 2. Follow the rule: SUB IN 1, CHECK IN 2:

Therefore when a= 3 and b= -2

5a - 2b = 19

5(3) -2(-2) = 19 **BE CAREFUL OF SIGNS**

15 + 4 = 19 which is correct.

11 months ago

Answered by Sophie, a GCSE Maths tutor with MyTutor

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