Question

solbe simulteneous equation problems

Answer 1

Answer of (iii)

Sum of two positive numbers (positive because a square of a number is always positive.) can be zero only when they both are zero.

Hence X - 5 = 0
Thus X = 5
Hence X - Y = 0
Thus Y = 5.

Therefore. X = Y = 5




Answer of (v)

Those two are equations of straight lines. The solution of two straight lines is the point at which they intersect. But we need a case where there is no solution. Hence these lines shouldn't intersect. Hence they are parallel. Hence their slopes are equal.

Line 1 : rx - 3y - 1 = 0
Rearranging

y = x(r/3) - (1/3)

Slope is r/3

Line 2 : (4-r)x - y + 1 = 0
Rearranging

y = (4-r)x + 1

Slope is (4-r)

But both slopes are equal.

r/3 = 4 - r

(4r/3) = 4

4r = 12

r = 3.