Question

Choose the equivalent system of linear equations that will produce the same solution as the one given below.

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

Answer 1

Have you solved systems of linear equations before? If so, do you have any ideas of where to start?

Answer 2

no i have idea

Answer 3

no idea**

Answer 4

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

Here's the steps to these kind of questions.
Step 1:
Choose one of the equation above and solve for one variable x or y (depends on your choice)

Step 2:
After you solve for, let's say X, you plug whatever you got for x into the second equation that you didn't began with.

Step 3:

When you plug in what you solved for x into the second equation, all the variables will become y.
You solve for y, and you'll get a number.
Plug that number to either one of the equations and see what you'll get for x.

If none of that seems familiar with you, then i will do my best to help and make you understand this.

Answer 5

Step 1: Which equation are you choosing from: ?
4x - y = -11
2x + 3y = 5

Answer 6

does it matter which one i choose

Answer 7

Nope. It does not matter.

Answer 8

Which equation is the easiest to solve for y?

Answer 9

I'd go with the easiest and i'll choose the first equation.

Answer 10

2x+3y=5
there is no negatives so its probably easier to solve

Answer 11

Okay, we'll go with that.

Answer 12

oops lol we can go with yours

Answer 13

Okay.

Answer 14

i'll choose the variable y because it's alone by itself. We can get rid of negatives when we divide both sides by negative :)

Answer 15

\(\large 4x - y = -11 \)
Subtract both sides by 4x
\(\large 4x-4x - y = -11-4x \)
\(\large - y = -11-4x \)
Divide both sides by -1
\(\Large \frac{- y}{-1} = \frac{-11-4x}{-1} \)
\(\large y = 11+4x \)

Answer 16

Makes sense?

Answer 17

what is y equal to now?

Answer 18

14x ? im sorry im so confused on this, and my teacher isnt responding

Answer 19

Why 14 x? We can't add 11 with 4x because they are different terms.

Y is equal to 11+4x, that's the only info we know

Answer 20

idk what to do

Answer 21

What does step 2 say?

Answer 22

After you solve for, let's say X, you plug whatever you got for x into the second equation that you didn't began with.

Answer 23

Yes. But let's not deal with x since we are dealing with y.

So, in different wording, we take whatever we got for y and plug it for the y in the second equation. Makes sense?

Answer 24

y=11+4x
Our second equation is
2x+3y=5

\(\large 2x+3(11+4x)=5 \)

Answer 25

2x+33+12x=5 ? or do you not use distributive property

Answer 26

Yes, you already distributed it

Answer 27

yup, you're right so far, now let's keep going

right now we have:

2x+33+12x=5

now add the x's together: 2x + 12x = __x

fill in the blank

Answer 28

how do i solve that? add or multiply?

Answer 29

so 14x

Answer 30

oh yeah sorry

Answer 31

yes, so now we have

14x + 33 = 5

subtract 33 from each sign

Answer 32

*from each side

Answer 33

-19=-28

Answer 34

am i supposed to subtract 33 from 33 too or no

Answer 35

not quite, remember that you can't combine variables and numbers

14x + 33 - 33 = 14x
5 - 33 = -28

14x = -28, make sense so far?

Answer 36

yes

Answer 37

14x = -28

divide both sides by 14

Answer 38

x=-2

Answer 39

good, we're almost done

we know that x = -2 now, so we can find y

let's go back to our first equation:

4x - y = -11

can you tell me what y is now?

Answer 40

-2

Answer 41

not quite. let's try plugging in -2 into the equation

4*(-2) - y = -11
-8 - y = -11

now can you tell me what y is?

Answer 42

no i dont understand

Answer 43

-8 - y = -11

add 8 to both sides, what do you get?

Answer 44

-y=-19

Answer 45

add, not subtract

-11 + 8 = ?

Answer 46

-3

Answer 47

right, so

-y = -3

what is y?

Answer 48

3

Answer 49

boom, we're done

x = -2 and y = 3
our solution is (-2,3)

Answer 50

thanks

Answer 51

Solve the system of equations by substitution. What is the solution for x?

2x + y = 1
4x + 2y = -2

can you help with this one too?