Question

find the value of k so that the pair of equations X + 2 Y is equal to 5 and 3 X + K Y + 15 is equal to zero has a unique solution​

Answer 1

What values of K does the pair of equations x-2y=3 and 3x+KY=1 have a unique solution?

First you have to write both equations and we will try to find a solution for this system of equations as a function of the value of K, so

X - 2Y = 3 and 3X + KY = 1

First multiply the first equiation by (3) and then sustract the second one,

3X-6Y=9

- (3X+KY = 1)

0X-(6+K) Y = 8

Y = -8 /(6+K)

here we have what we wanted, the value of Y as a function of K, now if you observe the resulting expression, there is just one value of K that we cannot use, that value is the one that made the divisor equal to zero, evidently is “-6”, so you can get a unique solution for this pair of equation “If and only if” K is not equal to -6.

Remember that one of the equations is variable so there will be a different solution for the equation set as you change the value of K, as soon as you change the value of K the solution for the system will change aswell.