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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. 

Sophie W. 11 Plus Maths tutor, GCSE Maths tutor, A Level Economics tu...

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