Question

**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

Answer 1

@manutd30

Answer 2

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

Answer 3

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

Answer 4

@DanJS what do you mean multiply them?

Answer 5

If you multiply an entire equation by a constant number, the equation is unchanged...

\[3*[4x-y=-11]\]

Answer 6

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

Answer 7

The result after multiplying the first by 3 is there, and now add the two together...

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

Answer 8

14x = -29

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

4x - 1y = -11
2x + 3y = 5

If added together, you just will get 6x + 2y = -6

Answer 13

you see that so far?

Answer 14

yes I see @DanJS

Answer 15

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...

Answer 16

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

Answer 17

you see what i mean ?

Answer 18

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

Answer 19

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

Answer 20

no, lets continue....

Answer 21

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

Answer 22

sorry

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

Answer 23

now add them together, both sides of the equals

Answer 24

14x=28!

Answer 25

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

Answer 26

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

that is it

Answer 27

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

Answer 28

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

Answer 29

One step further.....

Answer 30

Say you have one that has terms on the Y like this

... 3y = 10
... 2y = 41

Answer 31

How to get those to add and cancel out...

multiply the first by +2
Multiply the second by -3

Answer 32

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

Answer 33

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

Answer 34

That is it... good luck

Answer 35

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

Answer 36

welcome, practice.. hehe