**GOLD MEDAL WILL BE GIVEN TO WHO HELPS :) **
Choose the equivalent system of linear equations that will produce the same solution as the one given below.
4x - y = -11
2x + 3y = 5
A) -4x - 9y = -19
-10y = -30
B) 4x + 3y = 5
2y = -6
C) 7x - 3y = -11
9x = -6
D) 12x - 3y = -33
14x = -28

- anonymous

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- jamiebookeater

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- anonymous

@manutd30

- DanJS

multiply the first equation by 3 , then add them together...

- DanJS

The basic rules are, you can multiply an equation by a constant value
rearrange equations
and
add equations together...

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- anonymous

@DanJS what do you mean multiply them?

- DanJS

If you multiply an entire equation by a constant number, the equation is unchanged...
\[3*[4x-y=-11]\]

- DanJS

So when you do that then add the two together, a variable goes to zero and drops out

- DanJS

The result after multiplying the first by 3 is there, and now add the two together...
12x - 3y = -33
2x + 3y = 5
------------------

- DanJS

14x = -29

- DanJS

you want to find a number you can multiply each equation by, so that when added together, you have a variable drop out.
In this case -3y + 3y = 0y

- anonymous

@DanJS so I would have to do this to each one ?

- DanJS

Here i will do each basic step for this example.....

- DanJS

4x - 1y = -11
2x + 3y = 5
If added together, you just will get 6x + 2y = -6

- DanJS

you see that so far?

- anonymous

yes I see @DanJS

- DanJS

ok, so think of some number you can multiply one of the equations by , so that when added will result in zero for one variable...

- DanJS

if you multiply the first by 3, you will have a -3y in the first and a +3y in the second

- DanJS

you see what i mean ?

- DanJS

3*[4x - y = -11]
1*[2x + 3y = 5]
-------------------
that is the same as the original, you can multiply both sides of the equation by a number

- anonymous

@DanJS yes I see! so it would leave me with Answer B correct??

- DanJS

no, lets continue....

- DanJS

If you carry out what is above.. you get
12x - 3y = -11
2x + 3y = 5
----------------
That was the point, now when added the y term goes to zero

- DanJS

sorry
12x - 3y = -33
2x + 3y = 5
------------------

- DanJS

now add them together, both sides of the equals

- anonymous

14x=28!

- DanJS

right !, remember those two basic rules... and the goal of getting a variable to go to zero like the Y did here

- DanJS

Multiplying an equation by a constant number, and
Adding two equations together...
that is it

- anonymous

@DanJS this really helped, thank you for explaining this to me!

- DanJS

I could type all the dumb script rules in, but those are the ideas

- DanJS

One step further.....

- DanJS

Say you have one that has terms on the Y like this
... 3y = 10
... 2y = 41

- DanJS

How to get those to add and cancel out...
multiply the first by +2
Multiply the second by -3

- DanJS

6y
-6y
-----
0y

- DanJS

just take care of the X and right side of the = when you multiply through and add too

- DanJS

That is it... good luck

- anonymous

@DanJS wow you make this very easy, definitely writing these in my notes! thank you so much!

- DanJS

welcome, practice.. hehe

Looking for something else?

Not the answer you are looking for? Search for more explanations.