This post will teach you how to solve substitutional problem in mathematics. The term substitution in mathematics means, replacing a number from a particular given letter. This simply talks about when you are given a variable ( a number to replace).One thing about this operation is that, the given value should stand in other to work as the element.
Substitution in mathematics is very simple to understand and solve at any particular given time. Also, you must know BODNAS if really want to be a pro. In substitution, a value is always given as to replace the previous character. Now, i will solve some exercises on substitution.
Example 1
Given that, a = 3 , b = 5, c = - 4 and d = 6.Five the value of the following:
(1) 2a - b + 2c + d.
(2) 2(a² - b)-c + d²
3c + d²
(3) -----------
a - b²
(4) 12ab
Solution
(1) 2a - b + 2c + d.
= (2 x 3) - 5 + 2 x (- 4) + 6
= 6 - 5 + 2 - 4 + 6
= (6 + 2 + 6) - 5 - 4
= 14 - 9
= 5
Remember to apply the Rule of BODMAS, like what i did in the third steps.
(2) 2(a² - b)-c + d²
= 2(3² - 5) - (-4) + 6²
= 2 (9 - 5) + 4 + 36
= 18 - 10 + 4 + 36
= 18 + 4 + 36 - 10
= 58 - 10
= 48
Remember, - (-4) = + 4 -- (- x - = +).Also, 2(9 - 5) = 18 - 10.
3c + d²
(3) -----------
a - b²
3 x (-4) + 4²
= ---------------
3 - 5²
= -12 + 16
----------
3 - 25
4
= ------
-28
1
= ------
- 7
Example 2
1
T = ----- and T = 75 when n = 5.Find:
n
(a) T when n = 15
(b) n when T = 5
First : Let find the relationship between T and n.
1
T = ----- Where k is constant.
n
1
T = K x -----
n
Thus, T = 75 when n = 5
k
72 = -----
5
K = 5 x 75
K = 375
375
T = ------ the relationship between T and n
n
(a) T when n = 15
375
T = -------
n
375
T -------
15
T = 25
(b) n when T = 5
375
T = -------
n
375
n = -------
5
n = 75
1
r = ----- and r = 5 when S = 12
S
(a)Find the relation beween r and s.
(b) r when S = 20.
(c) S when r = 45.
1
r ----
S
1
r = k x ------
S
Where k is constant
k
r = -----
S
r = 5 , S = 12
k
5 = -------
12
k = 5 x 12
60
r = ------ relationship between r and S.
S
(b) r when S = 20.
60
r = ------
S
60
r = ------
20
r = 30
(c) S when r = 45.
60
r = ------
S
60
S ------
45
12
S -------
9
4
-------
3
1
S =1 -----
3
That is all about Substitution,Just follow up my lesson and will be a champion when its comes to mathematics.If you have questions, put them in the comment box.
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