Given the equations 9x+34y=6 and 2x+12y=9, by what factor would you multiply the second equation to eliminate y and solve the system through linear combinations?

Question

jdoe0001 · Answer

well.. you want to eliminate "y"

so your two "y's" are   34y and 12y

by what factor do you multiply the 2nd "y", or 12y
to eliminate "y",or to get a 0

well... call the factor.... "a"

we know then that, 12y * a
when added to 34y
gives 0

so   12y * a + 34y = 0

solve for "a",   see what you get

anonymous · Answer

Thank you I will do so :)

anonymous · Answer

Hmmm.. the answers contain a fraction and I am not getting a fraction in the multiple choice.

whpalmer4 · Answer

how about you verify that you typed the equations correctly, and tell us what the answer choices are?

anonymous · Answer

Well, yes I did type them correctly and the choices are: 
-4/3
-3/4
-3/2
and -7/2

whpalmer4 · Answer

Sorry, I apparently misread your response as "there aren't any fractions in the answer choices" but should have read it as "I get a fraction which isn't in the answer choices".  

I agree that the fraction I get is not on the list of choices.

anonymous · Answer

Yeah this math is so strange

whpalmer4 · Answer

Well, mostly strange because somewhere along the line someone made an error or the problem was otherwise corrupted.  Always frustrating to try to understand something new when the materials are incorrect!

anonymous · Answer

Yeah, I don't enjoy this kind of math and if I don't go through it I will fail my senior year :/. I am in desperate need of passing.

whpalmer4 · Answer

It isn't so bad once you get the hang of it.  You can always eliminate one equation by multiplying each equation by the opposite equation's coefficient of the variable you are trying to eliminate.

For example:

$$2x + 3y = 6$$$$3x + 4y=1$$If you want to eliminate $y$, multiply the first equation by 4, and the second equation by -3 (I changed the sign to make one result be negative).  

$$4*2x + 4*3y = 4*6$$$$-3*3x-3*4y=-3*1$$or$$8x+12y=24$$$$-9x-12y=-3$$

Notice now that we have equal but opposite coefficients for the variable we want to eliminate, and if we add the two equations together, we get

$$8x-9x+12y-12y=24-3$$$$-x+0y=21$$$$-x=21$$$$x=-21$$
Plugging that into one of the original formulas$$2(-21)+3y=6$$$$-42+3y=6$$$$3y=48$$$$y=16$$
So our solution is $(-21,16)$

That wasn't so bad, was it?

anonymous · Answer

Nah, but when you get a defective program that doesn't teach you the correct things. It's hard to work around. I understand better and will take notes though for the test. Thank you.

whpalmer4 · Answer

Good luck, I hope my explanation helped!