Question

43x+ 67y = -24 and 67x + 43y = 24 solve

Answer 1

Answer:

  (x, y) = (1, -1)

Step-by-step explanation:

We'll write these equations in general form, then solve using the cross-multiplication method.

  43x +67y +24 = 0

  67x +43y -24 = 0

∆1 = (43)(43) -(67)(67) = -2640

∆2 = (67)(-24) -(43)(24) = -2640

∆3 = (24)(67) -(-24)(43) = 2640

These go into the relations ...

  1/∆1 = x/∆2 = y/∆3

  x = ∆2/∆1 = -2640/-2640 = 1

  y = ∆3/∆1 = 2640/-2640 = -1

The solution is (x, y) = (1, -1).

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Additional comment

The cross multiplication method isn't taught everywhere. The attachment explains a bit about it. Our final relationship changes the order of the fractions to 1, x, y from x, y, 1. That way, we can use the equation coefficients in their original general-form order. (The fourth column in the 2×4 array of coefficients is a repeat of the first column.)