Solve the system using matrices. 3x + 4y = 18 3x + 4y = 18

Question

imstuck · Answer

Are you familiar with how to set up a matrix for this system of equations?

anonymous · Answer

no /.-

anonymous · Answer

I mean I do I just don't understand it

anonymous · Answer

Here are the possible answers:  
A. (-2, 6) 
 
 
B. (-2, -6) 
 
 
C. (6, -2) 
 
 
D. No solution

imstuck · Answer

Ok, let me help you set it up first. BOTH of your equations are 3x + 4y = 18?

anonymous · Answer

yes

anonymous · Answer

I know for a fact that the c is wrong

imstuck · Answer

Ok, that's kinda strange, but I will help.  Do you have a certain way you need to do this?  Using Cramer's method or finding the determinate first or just by using an equivalent matrix?

anonymous · Answer

its a work sheet . it just says Solve the system using matrices

imstuck · Answer

If it doesn't matter, let's set it up like this|dw:1401893743237:dw|where the 3's are the coefficients with the x's and the 4's are the coefficients with the y's.  The 18's are the solutions to both the equations.  Do you know that?

anonymous · Answer

yes

imstuck · Answer

The way we are going to do this is to do what we can to make this into the form|dw:1401893897677:dw|

imstuck · Answer

Are you familiar with that set-up?

imstuck · Answer

That means that we need to get the y position in the first equation to be a 0 and the x in the second equation to be a 0.  We will use mutiplication to do that.

anonymous · Answer

Umm no...  how you get 1 0
                                      0 1?

imstuck · Answer

I will show you.  It is multiplication.  In order to get the y in the second equation to a 0, you need to multiply it by something so that when you add it to the second equation it cancels out.  Right now the y in the first equation is a 4.  The y in the second equation is also a 4, but since they are both positive, they will add up to be 8, right?  If we multiply the whole first equation by a -1, the 4 now becomes a -4.

imstuck · Answer

|dw:1401894229910:dw|Actually, this is a HORRIBLE example because there is no solution to it.  If you do the math, all the x's and y's cancel each other out.  How dumb.  The answer to this is D.  Do you have another one that actually HAS a solution?  Do you have another problem like this?

anonymous · Answer

Yes hold up

imstuck · Answer

Gotcha.

anonymous · Answer

Well I don't got any good ones . that one was more difficult too me.

imstuck · Answer

Oh!  So you weren't sure what do with that?  It is no solution because all the variables canceled themselves out.  Good for you if you understand the concept, though because that was actually an easy one.  If you got the rest of it, you're good to go!

anonymous · Answer

Thanks I appreciate it!