Choose the equivalent system of linear equations that will produce the same solution as the one given below.
4x - y = -11
2x + 3y = 5

- anonymous

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- schrodinger

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- Zale101

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

- anonymous

no i have idea

- anonymous

no idea**

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## More answers

- Zale101

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.

- Zale101

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

- anonymous

does it matter which one i choose

- Zale101

Nope. It does not matter.

- Zale101

Which equation is the easiest to solve for y?

- Zale101

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

- anonymous

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

- Zale101

Okay, we'll go with that.

- anonymous

oops lol we can go with yours

- Zale101

Okay.

- Zale101

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 :)

- Zale101

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

- Zale101

Makes sense?

- Zale101

what is y equal to now?

- anonymous

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

- Zale101

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

- anonymous

idk what to do

- Zale101

What does step 2 say?

- anonymous

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.

- Zale101

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?

- Zale101

y=11+4x
Our second equation is
2x+3y=5
\(\large 2x+3(11+4x)=5 \)

- anonymous

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

- Zale101

Yes, you already distributed it

- Vocaloid

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

- anonymous

how do i solve that? add or multiply?

- anonymous

so 14x

- anonymous

oh yeah sorry

- Vocaloid

yes, so now we have
14x + 33 = 5
subtract 33 from each sign

- Vocaloid

*from each side

- anonymous

-19=-28

- anonymous

am i supposed to subtract 33 from 33 too or no

- Vocaloid

not quite, remember that you can't combine variables and numbers
14x + 33 - 33 = 14x
5 - 33 = -28
14x = -28, make sense so far?

- anonymous

yes

- Vocaloid

14x = -28
divide both sides by 14

- anonymous

x=-2

- Vocaloid

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?

- anonymous

-2

- Vocaloid

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?

- anonymous

no i dont understand

- Vocaloid

-8 - y = -11
add 8 to both sides, what do you get?

- anonymous

-y=-19

- Vocaloid

add, not subtract
-11 + 8 = ?

- anonymous

-3

- Vocaloid

right, so
-y = -3
what is y?

- anonymous

3

- Vocaloid

boom, we're done
x = -2 and y = 3
our solution is (-2,3)

- anonymous

thanks

- anonymous

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?

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