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Question
Form the simultaneous linear equations using the determinants
D = `|(4, -3),(2, 5)|`, Dx = `|(5, -3),(9, 5)|`, Dy = `|(4, 5),(2, 9)|`
Solution
If a1x + b1y = c1 and a2x + b2y = c2 are linear equations in two variables, then
D = `|("a"_1, "b"_1),("a"_2, "b"_2)|`, Dx = `|("c"_1, "b"_1),("c"_2, "b"_2)|`, Dy = `|("a"_1, "c"_1),("a"_2, "c"_2)|` ......(i)
Given, D = `|(4, -3),(2, 5)|`, Dx = `|(5, -3),(9, 5)|`, Dy = `|(4, 5),(2, 9)|`
Comparing these determinants with equation (i), we get
a1 = 4, b1 = – 3, c1 = 5
a2 = 2, b2 = 5, c2 = 9
∴ The required equations are 4x – 3y = 5 and 2x + 5y = 9.
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