Question

medal

Answer 1

How many solutions are there to the following system of equations?

3x – 9y = 0
–x + 3y = –3

A.
infinitely many

B.
2

C.
0

D.
1

Answer 2

divide everything in the first equation by -3.

Answer 3

then, re-write the system.

Answer 4

and then tell me what you think.

Answer 5

kk

Answer 6

y=x/3?

Answer 7

\(\large\color{royalblue}{ 3x – 9y = 0}\)

\(\large\color{red}{ \displaystyle \frac{\color{royalblue}{3x}}{3} \color{royalblue}{–} \frac{\color{royalblue}{9y}}{3} \color{royalblue}{=}\frac{\color{royalblue}{0}}{3}}\)

Answer 8

that is what I mean by dividing the equation by 3 , each term in it.

Answer 9

oh

Answer 10

and when you divide by -3, you do the same thing but with negative threes.

Answer 11

the lines are parallel.

Answer 12

maybe we can first deduce why?

Answer 13

Sonia, can you divide `3x-9y=0` by -3?

Answer 14

Divide each term by -3, (as I did with 3's, but you are doing with -3's ) and tell me what you get:

Answer 15

3x divided by -3 = -x
9y divided by =-3 = -3y
0 divided by =-3=0

Answer 16

yes, so as you divide `3x - 9y = 0` by -3,
YOU GET: `-x+3y=0`

Answer 17

So your first equation really is: \(\large\color{black}{ \displaystyle -x+3y=0 }\)
and the second one is: \(\large\color{black}{ \displaystyle –x + 3y = –3 }\) (we didn;t do anything to it, and don't need)

So you are given that \(\large\color{blue}{ \displaystyle -x+3y }\) is equal to \(\large\color{blue}{ \displaystyle 0 }\) in the first equation,
And you are given that (this very number, i.e) \(\large\color{blue}{ \displaystyle -x+3y }\) is equal to \(\large\color{blue}{ \displaystyle -3 }\) in the second equation.

Answer 18

Is there such a number \(\large\color{blue}{ \displaystyle -x+3y }\) that is equal to 0 and equal to -3 (at the same time) ?

Answer 19

click question above or below if you see question marks, and then come back here.
This will make question makrs symbols go away.

Answer 20

ok