A system of equations is shown below:

-3x + 7y = -16
-9x + 5y = 16

Part A: Create an equivalent system of equations by replacing one equation with the sum of that equation and a multiple of the other. Show the steps to do this. (6 points)

Part B: Show that the equivalent system has the same solution as the original system of equations. (4 points)

Question

A system of equations is shown below:

-3x + 7y = -16
-9x + 5y = 16

Part A: Create an equivalent system of equations by replacing one equation with the sum of that equation and a multiple of the other. Show the steps to do this. (6 points)

Part B: Show that the equivalent system has the same solution as the original system of equations. (4 points)

henrietepurina · Answer

@ParthKohli 
@Hero 
@undeadknight26

hero · Answer

Multiply the first equation by -3 then add it to the second equation.

henrietepurina · Answer

18x + -26y = 32 ???

hero · Answer

Not really

henrietepurina · Answer

Then what?

henrietepurina · Answer

@Hero

hero · Answer

What do you get if you multiplied both sides of the first equation by -3?

henrietepurina · Answer

x + (-21y) = 5.3
3x + (-1.6y) = -5.3

hero · Answer

Is this a new question you have posted?

henrietepurina · Answer

No, the same one

hero · Answer

If you don't know how to multiply, I'm not sure how much I'll be able to help you here.

henrietepurina · Answer

didn't i do it correctly?

hero · Answer

Let's start over...What is the first equation in the system?

henrietepurina · Answer

-3x + 7y = -16

hero · Answer

What result do you get after multiplying both sides of the first equation by -3?

henrietepurina · Answer

x + -21y = 48

hero · Answer

What happened to the coefficient of x?

henrietepurina · Answer

oh no, oops...
9 + -21y = 48

hero · Answer

Now the variable x is missing

hero · Answer

But anyway, you realize that you'll have

9x + -21y = 48

By the way, you should write these equations in their most simplest form:

9x - 21y = 48

hero · Answer

Anyway, take that result and add it to the second equation.

henrietepurina · Answer

ok.... - 26y = 32

henrietepurina · Answer

@hero amiright?

hero · Answer

Did you add or subtract? Looks to me like you added certain things but subtracted others.

henrietepurina · Answer

ohhh.... lemme try again

henrietepurina · Answer

-16y = 64

hero · Answer

That's better.

hero · Answer

So basically after you do that, you will be left with a system of 

-3x + 7y = -16
       -16y = 64

hero · Answer

Now all you have to do is show that the system:

-3x + 7y = -16
-9x + 5y = 16

Is equivalent to:

-3x + 7y = -16
       -16y = 64

henrietepurina · Answer

oh, so thats for 1?

henrietepurina · Answer

i meant a?

hero · Answer

If I have to answer that question, then it means you don't fully understand what I'm trying to explain to you.

henrietepurina · Answer

No, no I understand!

Part A: 
-3x + 7y = -16
-16y = 64

hero · Answer

Yes, that's for part A. But that's how you should have asked if you're going to ask. You ask it this way:

You say, 

"So is Part A:

-3x + 7y = -16
-16y = 64 ?"

And then, I will assume that you are only confirming what you already know.

henrietepurina · Answer

Yes :)

henrietepurina · Answer

Ok now im gonna get to part B...

hero · Answer

Okay, let me know how it goes

henrietepurina · Answer

-3x + 7y = -16
-9x + 5y = 16

9x + (-21y) = 48
-9x + 5y = 16

-21y) = 48
5y = 16

-16y = 64

henrietepurina · Answer

am i close @Hero

hero · Answer

That's the same thing we already did for Part A.

hero · Answer

In part B, what you should do is solve both systems using either elimination or substitution and see if you end up with the same (x,y) value for both systems.

henrietepurina · Answer

I dont get it?