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Question
Solve the following systems of linear equations by Cramer’s rule:
`3/2 + 2y = 12, 2/x + 3y` = 13
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Solution
Put `1/x` = a
⇒ 3a + 2y = 12
2a + 3y = 13
Writing the above equations in matrix form we get
`[(3, 2),(2, 3)][(x),(y)] = [(12, 13)]`
(i.e) AX = B
Now |A| = Δ = `|(3, 2),(2, 3)|` = 9 – 4 = 5 ≠ 0
Δa = `|(12, 2),(13, 3)|` = 36 – 26 = 10
Δy = `|(3, 12),(2, 13)|` = 39 – 24 = 15
a = `Delta_"a"/Delta = 10/5` = 2
y = `Delta_y/Delta = 15/5` = – 3
∴ a = 2, y = 3 but `1/x` = a
⇒ x = `1/"a" = 1/2` and y = 3
∴ x = `1/2`, y = 3
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