Question

ILL GIVE MEDALS
Solve the system by using elimination or elimination with multiplication. One point for the steps and one point for the correct solution.
3x + 4y = -2 and 2x - 3y = 10

Answer 1

combine like terms and sovle from there

Answer 2

can u show me the steps

Answer 3

@DI_KAZ that won't do the trick.

\[3x+4y=-2\]\[2x-3y=10\]

The thing to do here is find a pair of numbers such that you can multiply the first equation by one number and the second equation by the other number and end up with the coefficients of one of the variables being equal in magnitude but opposite in sign.

Answer 4

so -2 and 10 is the answer?

Answer 5

As 3 is not a multiple of 2, and 4 is not a multiple of 3, we don't have quite as easy a problem as we might, but no matter, it still isn't difficult. Just pick a column where the numbers are opposite in sign. Here that's the \(y\) column, with \(+4y\) and \(-3y\)

Answer 6

so can u write down the steps with the answer so i can see how u got it?

Answer 7

We multiply the first equation by 3, and the second equation by 4:

\[3*3x + 3*4y = 3*-2\]\[4*2x-4*3y=4*10\]

that becomes
\[9x + 12y = -6\]\[8x - 12y =40\]

Notice that the \(y\) column now has equal but opposite coefficients, and if we added that column, we would get 0.

Answer 8

so my answer is...?

Answer 9

That's exactly what we are going to do:

\[9x+12y = -6\]\[8x-12y=40\]--------------\[9x+8x + 12y-12y = -6+40\]What does that simplify to?

Answer 10

17x=54

Answer 11

-6+40 = 54? Are you sure?

Answer 12

\[-6+40 = 40-6 = 34\]
So we have \[17x=34\]Solve that for \(x\), please. What do you get?

Answer 13

umm idk

Answer 14

you don't know how to solve \[17x=34\]?

Answer 15

17 * <some number> = 34. What is <some number> that makes that true?

Answer 16

nvm i understand it

Answer 17

What do you get for the solution of the system?