Substitution Method-Simultaneous Equations

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Solve 2x - 9y = 0 …(i)

x - 18y = 27 … (ii)

From (i)

2x - 9y = 0

2x = 9y

…(iii)

Substituting this value of x in (ii), we get,

9y - 36y = 54

- 27y = 54 y = -2

Substitute this value of y in (iii):

= - 9

The solution is x = -9 and y = -2.

Solve 43x + 31y = 241 …(i)

31x + 43y = 277 …(ii)

By adding (i) and (ii), we get

74x + 74y = 518

x + y = 7 …(iii)

By subtracting (ii) from (i)

12x - 12y = -36

or x - y = -3 …(iv)

By adding (iii) and (iv) 2x = 4 x = 2

Substituting x = 2 in (iii), we get:

(2) + y = 7 y = 5

The solution is x = 2 and y = 5.

Solve: …(i)

…(ii)

Let and

(i) and (ii) can be written as

5a - 2b = 2 …(iii)

2a + 3b = 16 …(iv)

Multiplying (iii) by 3 and (iv) by 2, we get

15a - 6b = 6 …(v)

4a + 6b = 32 …(vi)

Adding (v) and (vi), we get 19a = 38 a = 2

Substituting a = 2 in (iv), we get

2(2) + 3b = 16

3b = 12 b = 4

Re-substituting

The solution is