Question

5. What is one value of “k” for which the homogeneous system has infinitely many solutions?

System: (5-k)x+y=0
2x+ (4-k)=0

Answer 1

or those really the equations?

Answer 2

are you missing a y in the second one?

Answer 3

I think you mean (5-k)x+y=0
2x+(4-k)y=0

Answer 4

in that case find the slopes of both lines
and set them equal

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if we have same slope and same y-intercept then we have infinitely many solutions

Answer 5

a1/a2=b1/b2=c1/c2 use this

Answer 6

Im doing this with matrices, I know how to do it with equations, and I know I need to get a row of "0s" to get infinitely many solutions, and I also know what it looks like on a graph. I need to know how to do it for my Linear Algebra class, and I can't seem to be able to use elementary row operations to find k.