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.
SW
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