Question

For what value of K will the following system of linear equations have a solution?
Will give a medal!!
2x + 6y= 4
x + 5y= 6
kx +5y= -2

Answer 1

First you figure the values of x and y from the the system of the first 2 equations. I will use elimination to solve for x and y through the first two given equations.

2x + 6y = 4
- 2x + 10y = 12
---------------
-4y = -8
y = 2 --> Now plug in this value in to one of the first equations and solve for x.

2x + 6(2) = 4
2x = 4 - 12
2x = -8
x = -4

Now we know that y = 2 and x = -4. Now we plug in these values in to the equation with k and solve for k.

k(-4) + 5(2) = -2
-4k + 10 = -2
-4k = - 12
k = 3

Therefore, k = 3 satisfies the above system of equations.