Question

Consider the system of equations

{ -2x + 6y = -8
{ cx _ 3y = -4

What value of c would produce a system that has an infinite number of solutions?
Justify your answer.

Explain why there is no value of c that would produce a system with no solution.

Enter your answer, justification, and explanation in the box provided.

Answer 1

hint: try multiplying equation 2 by 2

Answer 2

4

Answer 3

i had to change it

Answer 4

what is 2(3y)?

Answer 5

is the symbol in between cx and 3y supposed to be a minus sign?

Answer 6

6y

Answer 7

again, is the symbol in between cx and 3y supposed to be a minus sign?

Answer 8

yes

Answer 9

hm that actually changes things hold on

Answer 10

no

Answer 11

?

Answer 12

is it a minus sign or not?

Answer 13

no

Answer 14

so it's a plus sign?

Answer 15

yes

Answer 16

oh ok that makes sense then

Answer 17

i need like an explanation for those questions

Answer 18

{ -2x + 6y = -8
{ cx + 3y = -4

Answer 19

you would multiply equation 2 by 2 to get

2cx + 6y = -8

now put the two equations side by side

Answer 20

2x + 6y = -8
2cx + 6y = -8

what do you think c is equal to now?

Answer 21

c=−3y−4/x

Answer 22

hint: both equations are equal to each other

Answer 23

what value would c be if 2cx = 2x?

Answer 24

c = 1

Answer 25

awesome! c = 1 makes both equations equal, and therefore is your answer for a)

Answer 26

now, for b

in order for a system to have no solution, you would have to pick a value of c that makes both equations have equal slopes but different intercepts

as you have seen so far, if we set c = 1 and make the slopes equal, the y-intercepts are also equal, so there IS at least one solution, making it impossible for there to be 0 solutions

Answer 27

that should be sufficient to answer your problem I believe

Answer 28

ok could you help me some more ?

Answer 29

k