Question

For which values of the constant "k" does the system:
x - y = 3
2x - 2y = k
have no solutions? exactly one solution? many solutions? explain your reasoning.

Answer 1

so you want parellel lines this means
you want the same slope but different y-intercept

Answer 2

i'm talking about for the no solution part of the question

Answer 3

this is a system of linear equations question like matrixes and stuff

Answer 4

but both in this form y=mx+b

Answer 5

\[y=x-3\]
\[y=x-\frac{k}{2}\]

Answer 6

yes k = 6

Answer 7

so for no solution we need k/2=3

Answer 8

great! thats for the first part of the question

Answer 9

but you have to explain for which values of k results in no solutions, one solution and many solutions

Answer 10

yes we did the first part

Answer 11

now we are looking for exactly one solution which is impossible

Answer 12

so what is it no solutions, one solution or many solutions

Answer 13

these lines can either have infinitely many solutions are no solution

Answer 14

there is no value of k that will give us one intersection

Answer 15

oops i did the infinitely many part first

Answer 16

for infinitely many solutions k=6

Answer 17

for no solutions you want the y-intercepts to be different since the slopes are already the same

Answer 18

so for no solution k can be anything but 6

Answer 19

so how would i explain that there cannot be one solution?

Answer 20

because theses lines have the same slope

Answer 21

you can therefore only have infinitely many or no solution

Answer 22

infinitely many=same slope and same y-intercept
no solution= same slope and different y-intercept

Answer 23

one solution=different slope and a whatever y-intercept( same or different)

Answer 24

it is impossible here for that 3rd case i mentioned

Answer 25

I UNDERSTAND THANK YOU SOO MUCH :)

Answer 26

np :)