Question

Determine which system below will produce infinitely many solutions.
a) -6x + 3y = 18
4x - 3y = 6
b) 2x + 4y = 24
6x + 12y = 36
c) 3x - y = 14
-9x + 3y = -42
d) 5x + 2y = 13
-x + 4y = -6

Answer 1

C because 3x-y= 14 multiplied by -3 is -9x+3y= -42 so the equations are equal

Answer 2

not necessarily true...just because they have the same slope, does not mean they are equal equationa. You can have the same slope and different y intercepts and you will get a parallel line with no solutions.

Answer 3

texaschic101 you are correct. I was thinking about the lines having the same slope but forgot to mention about the y-intercept being the same too. I meant to add in if the y intercepts and slope was the same then the two will have infinite solutions It was a brain fart :-)

For instance Lets look at C:

3x - y = 14
y = 3x/1 - 14


-9x + 3y = -42
3y = 9x - 42
3y/3 = 9x/3 -42/3
y = 3x/1 - 14

Both equations have the same slope and they both have the same y-intercept and you can see they are equal to one another, which means the system will have infinite many solutions.

Answer 4

@texaschic101 you are correct. I was thinking about the lines having the same slope but forgot to mention about the y-intercept being the same too. I meant to add in if the y intercepts and slope was the same then the two will have infinite solutions It was a brain fart :-)

For instance Lets look at C:

3x - y = 14
y = 3x/1 - 14


-9x + 3y = -42
3y = 9x - 42
3y/3 = 9x/3 -42/3
y = 3x/1 - 14

Both equations have the same slope 3/1 and they both have the same y-intercept -14 and you can see they are equal to one another, which means the system will have infinite many solutions