Question

A student is trying to solve the set of two equations given below:
Equation A: x + z = 6
Equation B: 2x + 4z = 1
Which of the following is a possible step used in eliminating the z-term? Also, as I said before, could you explain your answer? Thanks guys >_<
 
 

Multiply equation B by 4.

Multiply equation A by 2.

Multiply equation A by –4.

Multiply equation B by 2.

Answer 1

The way that elimination works is that you add the two equations together. However, before you do so, you want to make sure that by doing so, a variable is eliminated. Here we want to eliminate z.

Due to like terms, only z terms will be able to add by each other. We have z on the top equation, and 4z on the bottom equation. In order to make 4z zero, we must subtract by 4z.

So if we add -4z to positive 4z, we will get zero. In order to get -4z on the top equation, what must we do to the top equation.

Answer 2

umm not quite sure :/

Answer 3

Example.

2a + b = 2
6a + 8b = 10

I want to eliminate 8b. So I multiply the top equation by -8

\[-8(2a + b = 2) \]
\[-16a -8b = -16\]

Now if I add the two equations, -8b and +8b cancel each other out.

Answer 4

Yes so we are left with the b?

Answer 5

from the 8s

Answer 6

No.

\[8b + (-8b) = 0\]

Answer 7

Or \[8b - 8b = 0\]

Same thing.

Answer 8

It's basically 8 of something minus 8 of the same thing.

Answer 9

Does that make sense to you?

Answer 10

yes it does

Answer 11

So what can we do to Equation A: x + z = 6, in order to take out the 4z on the bottom equation.

Answer 12

hmm

Answer 13

well if we ultiply the 2 by 2

Answer 14

by -2*

Answer 15

we would get -4 right?

Answer 16

and then the 4's cancel eachother out?

Answer 17

so z = 1?

Answer 18

@Shadow

Answer 19

ar you there??

Answer 20

No that's incorrect
Multiplying by -2 would cancel x out and Shadow said to cancel z out

Answer 21

oh ok

Answer 22

so what would I have to do?'

Answer 23

What could you multiply x + z = 6 with so that 4z in the second equation gets taken out?

Answer 24

6?

Answer 25

I am not good at math >_<

Answer 26

If you multiply the first equation by 6:
x + z = 6 -> 6x + 6z = 36
And then your second equation is 2x + 4z = 1
If you add them together
6x + 6z = 36
+2x + 4z = 1

Answer 27

oh

Answer 28

I'm not sure

Answer 29

It would be -4
-4x - 4z = -24
+ 2x + 4z = 1

Answer 30

11.5?

Answer 31

Yes

Answer 32

Now in either equation you can plug 11.5 for x
We'll use the first one
x + z = 6
11.5 + z = 6
Solve for z

Answer 33

-5.5?

Answer 34

Yep
Your question doesn't require to solve for this but I'm just showing you for later use

Answer 35

So back to your question

Answer 36

What did we do to x + z = 6 to get rid of z

Answer 37

multiplied by -4

Answer 38

So option C)

Answer 39

ok thx :D