Question

Solve the following system of equations.
1x+2y=5
-3x-6y=-15

Answer 1

I get 0=0. Have you learned matrices yet?

Answer 2

@RoLexx do you want me to show the work?

Answer 3

I got the same thing however how when i input the answer in its telling me im incorrect

Answer 4

0=0 is No Solution

Answer 5

0=0 actually means infinite amount of solutions

Answer 6

It is No Solution.

Answer 7

I just looked in my textbook just to make sure before I posted.

Answer 8

The directions say that If there are no solutions, type "No Solution" for both and . If there are infinitely many solutions, type "x" forx , and an expression in terms of x for y.

Answer 9

I've tried several times and I input x for x which is correct
but what expression do i need to input in terms of x for y?

Answer 10

Maybe my book is wrong.

Answer 11

x + 2y = 5
-3x - 6y = -15
Setting up a matrix
1 2 | 5
-3 -6 | -15 add (3 times row1) to row 2

1 2 | 5
0 0 | 0

y is arbitrary.

x + 2y = 5
y = s

x = -2s + 5
y = s True for all values of s. Infinite values of s

answer in matrix form
| x | = s | -2 | + 5 | 1 |
| y | | 1 | | 0 |

Answer 12

I actually multiplied one equation by another. I did not use a matrix. I do believe it to be No Solution.

Answer 13

Since the way I did it was specifically one of the ways you would normally do a problem like this.

Answer 14

substitution
x+2y=5
-3x-6y=-15

-3(-2y + 5) - 6y = -15
6y - 15 - 6y = -15
6y - 15 = 6y - 15
6y = 6y
y = y
for any value of y this will be correct. x will change with x of course, so infinite solutions

Answer 15

you r going to have to get a third opinion @RoLexx

Answer 16

I've tried that solution as well @ChmE

Answer 17

But it's incorrect i thank you and @MathLegend though for the advice.

Answer 18

if you put any value of y in the first equation and solve for x. you get the same x in the second equation using the same y. Infinite solutions

Answer 19

I said I could be wrong... but I looked at a problem in my textbook and it is just like this one where you get 0 = 0 and the answer says No Solution.

Answer 20

@Chme I looked in another place in my textbook and it says 0=0 is infinite solutions. So I believe @ChmE

Answer 21

Must have been read wrong by the publisher.

Answer 22

So is the book saying it is no solution because it is the same line and therefor you only have one equation with 2 unknowns and it can't be solved. I'd buy that

Answer 23

Just take the first one and say:
If x=x then:
x+2y=5 implies y=(1/2)(5-x)

Answer 24

It depends how you interpret the problem

Answer 25

But there is a solution, an infinite number of them. Given by the line.

Answer 26

It says that 0=0 is always true, there are infinitely many solutions.

Answer 27

I would put the answer as infinite

Answer 28

@malevolence19 thanks that correct but how did you get that (I'm curious)

Answer 29

Technically the answer is:
\[(x,y) \in \left\{(x,y) | y=\frac{1}{2}(5-x); x \in \mathbb{R}\right\}\]

Answer 30

I just took the first equation and solved for y. You have x, our "parameter" so you want y in terms of that x. Since both lines are the same you can solve using either, I just used the one without the extra -3 factor.

Answer 31

That explains it much better. Thanks :)