Math Is Fun Forum

SlowlyFading

Member

Registered: 2012-06-12

Posts: 149

Question Regarding Algebra and Simplifying

Okay, so I started reading the next lesson and a couple questions came up that I was hoping I could verify here.

The lesson states:

"Example 1: 2x + 3y = 6

  Step 1: put zero in for x and solve for y.

  2(0) + 3y = 6

  Simplify 2(0)

  0 + 3y = 6

  Simplify 0 + 3y

  3y = 6

Solve for y

3y =6

3    3

y = 2

The point is (0, 2)"

I understand what it's saying up until the, "Simplify 0 + 3y = 3y = 6" part. How is 3y simplified to 6? And then what happened here,
"3y =6
3    3
y = 2"

My last question is do you always put 0 in for x in an equation like this?

Thank you!

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I'm just here to get some help with an online math course I'm taking.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Question Regarding Algebra and Simplifying

hi SlowlyFading

Welcome to the forum! 

Let's start with your last question.  You have (2 times a number) plus (3 times another number) has to come to 6.

So no, you don't have to have x = 0.  There are lots of ways to make that come to 6.  Here's just a few:

I could go on.

What this question is asking for is "What does y have to be when x = 0, if the total must be 6?"

Now 2 x 0 makes 0 so we can write

And 0 + anything is just the anything.  Adding 0 won't change it so we can leave out the 0 altogether:

So 3 times something makes 6.  What is the something?

So y must be 2.

Hope that helps. 

Bob

ps.

And then what happened here,
"3y =6
3    3
y = 2"

I prefer to ask 3 times what? makes 6, but some people prefer this approach:

Both sides of the equation have been divided by 3.

When the numbers get more tricky that can be a more systematic way to get to an answer.

Looking at the (0,2) comment, it seems this work is heading towards straight line graphs.  Taking all the (x,y) values above and plotting them on a graph, look what happens.

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

eterry

Member

Registered: 2012-06-16

Posts: 4

Re: Question Regarding Algebra and Simplifying

2x+3y=6

x=0:  2(0)+3y=6

           0+3y=6

               3y=6

Not sure if I'm answering your question...?

eterry

Member

Registered: 2012-06-16

Posts: 4

Re: Question Regarding Algebra and Simplifying

Also, the method in this lesson is for finding intercepts.  So, yes, to find the intercepts you always start by letting x=0.

(In particular letting x=0 lets you find the y-intercept.)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Question Regarding Algebra and Simplifying

hi eterry

Welcome to the forum!

Well done for knowing what lesson this is from.  I admit I didn't when I posted my answer.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

SlowlyFading

Member

Registered: 2012-06-12

Posts: 149

Re: Question Regarding Algebra and Simplifying

Thank you Bob Bundy and eterry! I appreciate it. I understand now! Thanks.

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I'm just here to get some help with an online math course I'm taking.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Question Regarding Algebra and Simplifying

You are welcome.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob