Solve the following system of equations:
x − 2y = 6
2x − 4y = 10

- anonymous

Solve the following system of equations:
x − 2y = 6
2x − 4y = 10

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- anonymous

do you move the x to the other side first or do you just solve

- karatechopper

Well have you heard of substitution or elimination?

- anonymous

yes

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## More answers

- karatechopper

Which process do you prefer?

- anonymous

substitution

- anonymous

so the equation would look like this
2y=x-6

- karatechopper

What variable do you want to use?

- anonymous

x and y

- karatechopper

Okay pick one. :)

- anonymous

x-2y=6

- karatechopper

Lol tyler. I'm asking you to pick a variable that we can solve for in order to substitute.

- anonymous

oh lol x

- karatechopper

ahah alrighty then.

- karatechopper

x − 2y = 6
Solve that equation for x now. :)

- anonymous

so you would substitute 0 for x and the equation
(0)-2y=6

- karatechopper

nooooooooooooo

- karatechopper

where have you go that my friend

- karatechopper

Solve for x :)

- anonymous

oops

- anonymous

x-2(0)=6

- anonymous

x=6

- karatechopper

.uhm.
We need to isolate x
x − 2y = 6
Add 2y to both sides in order to make x be on its own.
Whats x= now?

- anonymous

x=2y+6

- karatechopper

YAY! :D

- karatechopper

Okay now let's look at the second equation.

- karatechopper

2x − 4y = 10

- anonymous

ok

- karatechopper

We know that x=2y+6
Now plug that value for x into this equation
2x − 4y = 10

- anonymous

ok so 2(2y+6)-4y=10

- anonymous

4y+12-4y=10

- anonymous

8y+12=10
8y=-2

- karatechopper

Wait a minute..

- karatechopper

2(2y+6)-4y=10
4y+12-4y=10
4y-4y=0
12=10
Dang we did something wrong.

- anonymous

yeah maybe we entered the wrong equation

- karatechopper

uhm lets try solving for x in the bottom equation?
2x-4y=10

- karatechopper

actually don't...it won't work again.

- karatechopper

Are you okay if we try elimination?

- anonymous

yeah sure

- karatechopper

Yay.
x − 2y = 6
2x − 4y = 10
Okay so let's try to eliminate x, we will multiply the top equation by -2, Could you do that for me please?

- anonymous

yay

- anonymous

you multiply everthing by two or what

- karatechopper

yes by -2

- anonymous

ok so -2x-(-4)y=-20

- karatechopper

what is 6 x -2?

- karatechopper

We just wanted to multiply x-2y=6
You should have gotten
(-2)x-(-2)(2)y=6(-2)

- anonymous

-2x-(-4)y=-12

- karatechopper

okay what is a negative times a negative

- anonymous

positive

- anonymous

so its a positive 4y

- karatechopper

yes

- karatechopper

now rewrite the equation we have.

- anonymous

-2x+4y=-12

- karatechopper

Alright turn up.

- anonymous

yay

- karatechopper

So lets rewrite the whole thing.
-2x+4y=-12
2x − 4y = 10
Now, solve it out. As you can see...both variables cancel out...
Did you post the right question?
Also, the answer because we cannot solve it is....
No solution.

- anonymous

?
Show that the solution to the system of equations 10x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations
Show that the solution to the system of equations 10x − 2y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations
Show that the solution to the system of equations 11x − y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations
Show that the solution to the system of equations 11x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations

- karatechopper

Woah there amigo, what is this?

- anonymous

the answers

- karatechopper

What?
Those look like dif questions,
I am confused.

- anonymous

ok look at this

- anonymous

A system of equations is shown below:
6x − 2y = 3 (equation 1)
5x + 3y = 4 (equation 2)
A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. If equation 2 is multiplied by 1, which of the following steps should the student use for the proof?
Show that the solution to the system of equations 10x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations
Show that the solution to the system of equations 10x − 2y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations
Show that the solution to the system of equations 11x − y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations
Show that the solution to the system of equations 11x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations

- anonymous

thats the whole question

- karatechopper

@TheSmartOne Will try to help you for a bit, I've got to finish something else. Hope I was some sort of help. Sorry.

- anonymous

your fine you were help @karatechopper

- TheSmartOne

which question are we working on?

- anonymous

the one up above

- anonymous

but ill show you it just in case you didnt see it

- anonymous

- TheSmartOne

It's an interesting problem, hmmmm.

- TheSmartOne

can you add these 2 equations and tell me what you get:
6x − 2y = 3
5x + 3y = 4

- anonymous

ok

- TheSmartOne

so basically, what is
6x + 5x -2y + 3y = 3 + 4

- anonymous

yeah sorry i was doing something else

- anonymous

11x-y=7

- TheSmartOne

and which answer choice has 11x-y=7 ?

- anonymous

the third and the fourth one

- anonymous

C and D

- TheSmartOne

C has 11x \(\bf\color{red}{−}\) y = 7
D has 11x \(\bf \color{red}{+}\) y = 7

- anonymous

so the answer is C

- anonymous

@TheSmartOne

- TheSmartOne

correct

- anonymous

awesome thank you

- TheSmartOne

np :)

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