Algebra 2

Substitution in an equation is all about plugging in or putting in particular values for one or more terms in an equation in order to work out a total. Why would we want to do this?
Suppose I have two walks that I do regularly - one in the Brecon Beacons, and one near Abergavenny. And suppose that last month I did the Brecon walk 5 times and the Abergavenny walk 3 times. If I know how far the two walks are - say the Brecon one is 10 miles and the Abergavenny one is 8 miles - I might be curious to know how far I walked in total last month. This is what substitution is all about. In this example I can form the expression
5b + 3a
(5 for the number of times I did the Brecon walk and 3 for the number of times I did the Abergavenny walk) and then plug in or substitute 10 for b and 8 for a to get
5x10 + 3x8 = 74
so I walked 74 miles in total.

NB Care needs to be taken with negative numbers, particularly where we have to subtract a negative. Remember the rules:
i adding a positive number equals addition (+ + = +)
ii adding a negative number equals subtraction (+ - = -)
iii subtracting a positive number equals subtraction (- + = -)
iv subtracting a negative number equals addition (- - = +)
Rule iv is the one that catches most people out. Examiners know this - see Example 6 below.
Example 1
Evaluate 3a-2 when a=3.
Solution: Putting in a=3, we get 3x3-2 = 9-2 = 7.
Example 2
Calculate 3h+2j when h=-2 and j=-1.
Solution: Putting in h=-2 and j=-1, we get 3x(-2)+2x(-1) = -6-2 = -8.
Example 3 (Foundation Nov 15 Paper 1 Q5(b) )
Use the formula P=5A-6B to find the value of P when A=7 and B=4. (Answer = 11)
Example 4 (Foundation Nov 14 Paper 1 Q9(c) )
Find the value of 2p+5q when p=-3 and q=2. (Answer = 4)
Example 5 (Foundation May 15 Paper 1 Q5(b) )
Use the formula W=7R-3T to find the value of W when R=5 and T=9. (Answer = 8)
Example 6 (Foundation June 14 Paper 1 Q5(c) )
Find the value of p=3a+4b-6c when a=2,b=3 and c=-1. (Answer = 24. If you get 12, remember that - - = +)
Example 7
Find the value of r=2a/b when a=4 and b=8. (Answer = 1)
Example 8
Find the value of z=a2 + b - 3c when a=3, b=2 and c=-2. (Answer = 17. Again, watch out for the __. If you get 5, think again!)