Question

What is the condition that pair of linear euqations $kx+2y=5$ & $3x+y=1$ have unique solution?

Answer 1

Given that equations are kx + 2y = 5

3x + y = 1

kx + 2y = 5

2y = 5 -kx

y = 5 -k/2

3x + y = 1

y = 1 - 3x.

These are the equivalent lines in the slope intercept form. Their slopes would be equal . If these lines were parallel and they would have no common point . Therefore , no solution for this type of equation .

slpoe intercept form y = mx + c

y = 5 - k/2

y = 1- 3x

-k/2 = -3

k = -3 * -2

k = 6.

so , the answer is 'there is no solution '