Giving Lessons: Solving Systems of Equations by Substitution

Question

aihberkhan · Answer

if you don’t already know… for the past few days I have decided to start Giving Lessons. If you want to see the rest of them just go on my profile, click on my questions, and click on the ones that start with: “Giving Lessons”. I feel that this is definitely helping some of you, so I decided that this is a great way to help you guys out! If you already know this, then tag someone who doesn’t, but if you don’t already know this, then hopefully this will help you out!

I have noticed for the past few days, an increase in “Systems of Equations” questions. That is why… if you see someone that asks a “Systems of Equations” question, give them the link to this post please! Also, if you really need help in this subject, then hopefully this will help you out! 

Alright! Lets begin, shall we? So our first sample problem is:

$$y = 6x - 11$$
$$-2x - 3y = -7$$

Okay, so those are our two equations that we will be working with today. In these types of problems you are solving for the variables in the equations. So today we will be solving for: 

$$x$$
and
$$y$$

First, we need to find y. Since the 1st equation already gives us what “y” is, then we can plug in that equation INTO the second equation. That is where substitution comes in. We are going to substitute y with the 1st equation. But keep in mind, that is not the actual value of y. When we do that, the second equation should become:

$$-2x - 3(6x - 11) = -7$$

Now, we will solve that equation for x. When we do that we should get:

$$x = 2$$

Great! We now have the value of x! Now we are going to plug in that value of x into the first equation. When you do that you should get:

$$y = 6(2) - 11$$

Lastly, just solve that equation and you should get:

$$y = 1$$

Awesome! We know have the value of both x and y! Now we just need to put the answer in coordinate form. So our COMPLETE answer is:

$$(2, 1)$$ 

We always want to make sure we write our answer like that.

DONE! GREAT JOB! :)

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Still Confused? Don’t worry! We will be doing one LAST sample problem!

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Alright. Our last sample problem is:

$$-7x - 2y = -13$$
$$x - 2y = 11$$

First, lets find x since it’s a shorter process to find. All we do is subtract 2y from both sides in the second equation When you do that, you should get:

$$x = 2y + 11$$

We have found x. Now we can plug this equation and substitute x for this equation in the first equation. But keep in mind, this is not the actual value of y. When we do substitute it, the first equation would become:

$$-7(2y + 11) - 2y = -13$$

Now, we will solve that equation for y. When we do that we should get: 

$$y = -4$$

Great! We now have the value of y! Now we are going to plug in that value of y into the second equation. When you do that you should get:

$$x - 2(-4) = 11$$

Lastly, just solve that equation and you should get:

$$x = 3$$

Awesome! We now have the value of both x and y! Now we just need to put the answer in coordinate form. So our COMPLETE answer is:

$$(3, -4)$$

We always want to make sure we write our answer like that. 

DONE! GREAT JOB! :)

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Still Confused? Don’t Worry! If you have any questions just comment them down below! I will try my best to answer them as soon as possible! 

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Also, if you need extra help… just go to 

aihberliterally.wix.com/aihberliterally

to book your FREE tutoring lessons!

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Thanks for reading! Have an amazing day/afternoon/evening… or whatever :) 

I hope this helped you in some way! Once again, If you already knew this, then tag someone who doesn’t. But if you didn’t and this helped you… then I am very glad that I helped you out! 

Alright, bye now! Love you lots! :)

aihberkhan · Answer

@ganeshie8 @Michele_Laino @Luigi0210 @AlexandervonHumboldt2 @sleepyjess @CGGURUMANJUNATH @KendrickLamar2014 @amistre64 @campbell_st @tkhunny @thomaster @freckles @whpalmer4 @Vocaloid @ikram002p @micahm @Jaynator495 

You guys probably don't need this lesson, because you are all so smart! But I am just giving these lessons. So if you need this, then I am glad it helped! But if not, you can tag someone if you like. I just wanted to show you guys, because I hope to be up at your level someday! :)

vocaloid · Answer

yay good job ~

kendricklamar2014 · Answer

Nice tutorial @AihberKhan I love this :)

aihberkhan · Answer

Thank you! @KendrickLamar2014

kendricklamar2014 · Answer

:D

amistre64 · Answer

nice explanations.  yet i find that the most difficult part people have is the part that you glossed over.  solving 1 equation in 1 unknown.