What is the value of the x variable in the solution to the following system of equations?

2x − 3y = 3
5x − 4y = 4

−1

0

x can be any number as there are infinitely many solutions to this system

There is no x value as there is no solution to this system

Question

What is the value of the x variable in the solution to the following system of equations?

2x − 3y = 3
5x − 4y = 4

 −1

 0

 x can be any number as there are infinitely many solutions to this system

 There is no x value as there is no solution to this system

e.mccormick · Answer

OK, so which did you get?  I'll test it myself and see.

anonymous · Answer

1 min.

anonymous · Answer

it's c

e.mccormick · Answer

So you say infinite?

anonymous · Answer

yeah

e.mccormick · Answer

That would mean they were the same line. But if you put it in y=mx+b form, they are not the same. Two ways to pretty easily solve this. First, subtract the one equation from the other, this gets you to a single y, then you can solve for y in terms of x and sub that bak in. The second is to graph it: https://www.desmos.com/calculator/kjcc8nvrd8 After looking at the graph, do you have a different answer?

e.mccormick · Answer

I'm taking linear algebra, so I put it in a matrix and solved that way, but all the methods should get the same answer.

anonymous · Answer

damn.. lol

e.mccormick · Answer

So you get it now?

anonymous · Answer

I thinks A then

e.mccormick · Answer

B: The point (0,-1) and they are asking for x.

e.mccormick · Answer

But I have confused my X and Y so many times I get why anyone would make that mistake.  Heck, I still mess up my X and Y!

anonymous · Answer

ooh! I get mixed up sometime lol

e.mccormick · Answer

Now, want to see it worked in algebra, or do you think you have it?

anonymous · Answer

it's up too you really.

e.mccormick · Answer

I am fine with working it.$$2x-3y=3\ -(5x-4=4)$$ so I am subtracing to start. $$2x-3y=3\ -5x+4=-4$$ which gets me:$$-3x+y=-1$$ With me so far?

e.mccormick · Answer

I did that to get y down to just y.  It is a valid thing to mix together the two eqations. Now I solve for that y.$$y=3x-1$$  There, I kind of know what y is.  I know what y is as x.  So I can substitute into either of the original ones and get something useful.

e.mccormick · Answer

$$2x-3(3x-1)=3$$ is a good place to start.  That simplifies and solves:$$2x-9x+3=3\ -7x=0\ x=0$$

e.mccormick · Answer

If they also needed y, I could now put 0 in for x on either of the above, and solve for y.  It is -1.

e.mccormick · Answer

I hope that helps!

anonymous · Answer

wow thanks! helped so much!

e.mccormick · Answer

Math is one of those thigns where there are lots of different ways.  Probably eight of them would solve this.  The thing is to find one or two that make sense to you, then you can always do it.  Have fun!

anonymous · Answer

I'll take that into consideration! thanks:D