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| Substitution Method |
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| Solve 2x - 9y = 0 …(i) |
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| x - 18y = 27 … (ii) |
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| From (i) |
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| 2x - 9y = 0 |
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| 2x = 9y |
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 …(iii) |
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| Substituting this value of x in (ii), we get, |
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| 9y - 36y = 54 |
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- 27y = 54  y = -2 |
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| Substitute this value of y in (iii): |
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| = - 9 |
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 The solution is x = -9 and y = -2. |
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| Solve 43x + 31y = 241 …(i) |
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| 31x + 43y = 277 …(ii) |
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| By adding (i) and (ii), we get |
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| 74x + 74y = 518 |
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| x + y = 7 …(iii) |
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| By subtracting (ii) from (i) |
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| 12x - 12y = -36 |
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| or x - y = -3 …(iv) |
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By adding (iii) and (iv) 2x = 4  x = 2 |
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| Substituting x = 2 in (iii), we get: |
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(2) + y = 7  y = 5 |
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 The solution is x = 2 and y = 5. |
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Solve: …(i) |
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 …(ii) |
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Let  and  |
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 (i) and (ii) can be written as |
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| 5a - 2b = 2 …(iii) |
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| 2a + 3b = 16 …(iv) |
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| Multiplying (iii) by 3 and (iv) by 2, we get |
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| 15a - 6b = 6 …(v) |
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| 4a + 6b = 32 …(vi) |
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Adding (v) and (vi), we get 19a = 38  a = 2 |
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| Substituting a = 2 in (iv), we get |
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| 2(2) + 3b = 16 |
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3b = 12  b = 4 |
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| Re-substituting |
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 The solution is  |
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