Form the simultaneous linear equations using the determinants D = |4-325|, Dx = |5-395|, Dy = |4529| - Algebra

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Sum

Form the simultaneous linear equations using the determinants

D = `|(4, -3),(2, 5)|`, Dx = `|(5, -3),(9, 5)|`, Dy = `|(4, 5),(2, 9)|`

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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.

  Is there an error in this question or solution?
Chapter 1: Linear Equations in Two Variables - Q.5

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