Question

How many solutions are there to the following system of equations

Answer 1

What have you done so far on this problem?

Answer 2

Nothing, I don't understand how I can check how many solutions that has..

Answer 3

Well, have you tried to find the solution(s)?

Answer 4

Do you know what it means to be a solution to a system of equations?

Answer 5

I punched the numbers in the a graph calculator and this is what I see, so that's why I think the correct answer is D.2

Answer 6

what you have circled(marked), are the x and y intercepts for one line.

Answer 7

If you read this http://www.purplemath.com/modules/systlin1.htm
You will find how to determine your answer.

Answer 8

I still don't get it...

Answer 9

Divide the second equation by -3.

Answer 10

x=1+3y

y=x-1/3

Answer 11

@SolomonZelman Solve for y or x?

Answer 12

Did you read what I linked to?

Answer 13

Yes, and here is my math...

Equation 1: 3x-9y=0
Equation 2: -x+3y=-3

Multiply Equation 2 x 3:
-3x+9y=-9
Therefore,

3x-9y=0
-3x+9y=-9
~~~~~~~
0=-9

So B is correct then, right?

Answer 14

@FibonacciChick666 and @SolomonZelman

Answer 15

do the lines intersect?

Answer 16

on the graph, do the lines cross each other at all?

Answer 17

No not at all

Answer 18

ok, so how many solutions are there?

Answer 19

(Because, your math is correct, but you never formed a conclusion statement)

Answer 20

There are 0 solutions..

Answer 21

right, so now. Just remember that when you show your work you need a conclusion statement. You have to tell us what the work was for/means

Answer 22

So the answer is B, right?

Answer 23

Sorry, I got called away.

Yes, a solution to a system of equations is a point which is in common to all of the equations. A system of linear equations (equations whose graphs are lines) will have either 1 solution (all the lines intersect in a single point), 0 solutions (the lines are parallel and never intersect) or infinitely many solutions (the lines are the same, and each of the infinitely many points that make them up is a solution).

One way to see if you will have any solutions (in addition to just solving and counting) is to find the slope of each line. If the slopes are different, the lines intersect. If the slopes are identical, they are either parallel or coincident. Parallel lines have the same slope, but a different y-intercept.

You had \[3x-9y= 0\]\[-x+3y=-3\]With the equations in this form, you can find the slope by dividing the x coefficient by the y coefficient:

\[m_1 = \frac{3}{-9} = -\frac{1}{3}\]for the first equation and
\[m_2 = \frac{-1}{3} = -\frac{1}{3}\]for the second equation

They have same slope, so there are either no or infinitely many solutions.

To tell which case, multiply one or both of the equations by whatever convenient factor will make the coefficients equal. If we multiply the second equation by \(-3\), we get \[(-3)(-x) + (-3)(3y) = (-3)(-3)\]\[3x-9y=9\]comparing that with the other equation, we can see that the coefficients of \(x\) and \(y\) are identical, but the value on the other side of the equal sign is different. That means the lines are parallel, and there no solutions.

Answer 24

Okay. Thank you!