Question

If `|(1, y),(4, x)|` = 12 and `|(-1, 2),(y, x)|` = 6, from the given determinants, form the two simultaneous equations in x and y and solve them.

Answer 1

Given: `|(1, y),(4, x)|` = 12 and `|(-1, 2),(y, x)|` = 6

⇒ x – 4y = 12   ......(i)

And – x – 2y = 6  ......(ii)

Adding equations (i) and (ii), we get

   x – 4y = 12
– x – 2y = 6   
      – 6y = 18

⇒ y = `(-18)/6` = – 3

Putting the value of y in equation (i), we get

x – 4(– 3) = 12

⇒ x + 12 = 12

⇒ x = 12 – 12

⇒ x = 0

Hence, x = 0 and y = – 3.