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Question
Solve the following systems of linear equations by Cramer’s rule:
5x – 2y + 16 = 0, x + 3y – 7 = 0
Solution
The above equations are 5x – 2y = – 16 and x + 3y = – 7
The matrix form of two above equations is
`[(5, -2),(1, 3)] [(x),(y)] = [(- 16),(7)]`
(i.e) AX = B
Now |A| = Δ = `|(5, -2),(1, 3)|` = 15 + 2 = 17 ≠ 0
Δx = `|(-16, -2),(7, 3)|` = – 48 + 14 = – 34
Δy = `|(5, -16),(1, 7)|` = 35 + 16 = 51
Now x = `Delta_x/Delta = (-34)/17` = – 2
y = `Delta_y/Delta = 51/71` = 3
So, x = – 2, y = 3
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