Question

For what values of k do the following three lines have a common point of intersection? {x+y=12 {k x-y =0 {y-x=2k

Answer 1

The three lines have a common point of intersection for any value of k.

Step-by-step explanation:

To find the values of k for which the three lines have a common point of intersection, we need to solve the system of equations:

x + y = 12

kx - y = 0

y - x = 2k

First, let's rewrite the second equation as y = kx. We can substitute this into the other equations to eliminate y:

x + kx = 12

y - x = 2k

Combining like terms, we get:

(1 + k)x = 12

2k + x = y

Now, we can substitute y = 2k + x into the first equation:

x + kx = 12

(1 + k)x = 12

This equation holds true for all values of x and k, so the three lines have a common point of intersection for any value of k.