Question

Multiply one of the equations, 3x-y=0 and 5x+2y=22, by a constant in order to solve by elimination. Show the new system of equations.

Answer 1

Do you understand how elimination works?

Answer 2

no :(

Answer 3

OK. To eliminate is to remove. The goal is to remove either x or y from one equation so you know what one of the variables is because it will be alone.

Answer 4

okay so i did that with the first equation and got y=11-5x. is that correct?

Answer 5

That would be for substitution, rather than elimination. In elimination you write them out like this:

\(\begin{array}{rrr}
3x&-y=&0 \\
5x&+2y=&22
\end{array}\)

It sets them up for being added together.

Answer 6

8x+y=22?

Answer 7

Now, if you look at them that way. What would you have to do to one of the equations to make it that when they are added in columns that one of the variables would disappear? It is in your instructions.

Answer 8

oh, would i multiply 2 for the y's to make it cancel out the postiive 2?

Answer 9

Yes! Which is the elimination part! You kill the y in this case to learn what the x is.

Answer 10

okay so, so would the answer be x=2?

Answer 11

\(\begin{array}{rrr}
3x&-y=&0 \\
5x&+2y=&22
\end{array}\)

\(\begin{array}{rrr}
2\cdot 3x&2\cdot (-y)=&2\cdot 0 \\
5x&+2y=&22
\end{array}\)

\(\begin{array}{rrr}
6x&-2y=&0 \\
5x&+2y=&22
\end{array}\)

\(11x=22\)

\(x=2\)

Yep.

Answer 12

woohoo! thank you!!! :)

Answer 13

Then you can substitute back that to find a y if they need it. But I think what they may be looking for is that middle part of \(11x=22\)

Answer 14

so if it says "combine the two equations to eliminate one of the variables" how would i go about that?

Answer 15

Or even the step before that!

Ah ha. Yah, you did it all and they only wanted the first step.

Answer 16

See, for the first question, all they want is:
6x−2y=0
5x+2y=22

Then the second question is asking you to do the part to get the:
11x=22

Answer 17

oh okay! thank you so much for helping me out! i realllly appreciate it :)

Answer 18

np. Have fun!

Answer 19

hehe thanks! but the last step says "substitute the value you found back into an equation to solve for the other variable" so would it be something like since x=2, 3(2)-y=0. 6-y=0-y=-6 (-1) = y=6?

Answer 20

Yes. That or put it in the other, but that is eaiest. If you work th other one, you should get the same exact answer.

Answer 21

okay thank you :)