Question

How many solutions does this system of equations have?



3x – 4y = 12

y = 4x – 3

A. 0
B. 1
C. 2
D. infinite

Answer 1

you make no sense

Answer 2

you can use substitution.

Answer 3

How many solutions does this system of equations have though not solving the equation

Answer 4

solving the equation is one way to find out

Answer 5

oh ok sorry i'm still asleep

Answer 6

the first equation can be re-arranged
3x – 4y = 12
3x = 12 + 4y
4y = 3x - 12
y = 3/4 -12

Answer 7

so we have these two equations:
y = 3/4x -12
y = 4x – 3

Answer 8

you can't see at one sight how many solutions they have

Answer 9

so I can just solve the system instead :)
3x – 4y = 12 ,plug y=4x-3

3x - 4(4x-3) = 12
3x -16x +12 = 12
3x-16x = 0
-13 x = 0

x = 0.....

Answer 10

y = 4x – 3
y = -3

3x – 4y = 12
-4y = 12
y = -3

there seems to be a solution

Answer 11

Oh I see haha thank you

Answer 12

no problem, I'm still trying if elimination gives more information

3x – 4y = 12
y = 4x – 3

– 4y = -3x + 12
y = 4x – 3

– 4y = -3x + 12
4y = 16x – 12
------------
0 = -9x

Answer 13

looks like x really is 0........and y=-3

Answer 14

ok i'm once again confuzzled

Answer 15

its because we dont follow rules...........

do you know any rules for the outcome of substitution?
I believe ifyou substitute two equations
and you get a distinct value, then the system has 1 solution

Answer 16

at least if the solution works in both equations, which we have checked :)

Answer 17

y - x = 9
2 y - 2x = 18

this system has infinite solutions
what happens when subsituting?

the first equation can be written as y = 9 + x, then substitute:
2 ( 9+x ) -2x = 18
18 + 2 x - 2 x = 18
18 = 18

look at this: if you get a solution like this, then it has infinite solutions

Answer 18

oh ok thank you but i'm litterally falling asleep I'll just do this stuff after a couple hours thank you so much