find the value of k for which the following system of equations has a unique solutions 1. kx + 2y = 5, 3x+y=1

If you choose any value for k other than 6, that will be give you the one solution.

If k=6, you have no solutions because the lines will be parallel.

Step-by-step explanation:

We are going to put each of this in y=mx+b where m is the slope and b is the y-intercept.

kx+2y=5

Subtract kx on both sides:

2y=-kx+5

Divide both sides by 2:

y = (-k/2) x + (5/2)

The slope is - k/2 and the y-intercept is 5/2

3x+y=1

Subtract 3x on both sides:

y=-3x+1

The slope is - 3 and the y-intercept is 1.

We want the system to have one solution so we want the slopes to be difference.

So we don't want (-k/2) = (-3).

Multiply both sides by - 2: k=6.

We won't want k to be 6.