Solving systems of equation

I really don't know how to solve this system of equation, it's nothing I've ever done before.... mostly they would have identical and the same amount of variables in every column but this one doesn't....

x + 10 + y + 36 = 210

80 + 10 + z + y = 180

36 + z + y + t = 220

Re: Solving systems of equation

Collect like terms, then it will be in a somewhat more familiar format.

Re: Solving systems of equation

10x + 36y = 210

80z + 10y = 180

36z + yt = 220

LIKE THAT???

Re: Solving systems of equation

No, not like that. You have switched some additions to multiplications. Let's take the first one: x + 10 + y + 36 = 210 where we can subtract the 10 and the 36 from both sides to give x + y = 164. Follow that process with the other two and see where it takes you.

Re: Solving systems of equation

x + y = 164

z + y = 90

z + y + t = 184

like that??? if it is, then now what?

Re: Solving systems of equation

No, we cannot change addition to multiplication like that.

We have:

$\displaystyle x+10+y+36=210$

$\displaystyle 80+10+z+y=180$

$\displaystyle 36+z+y+t=220$

Now, if we subtract all the constants on the left side of each equation from the right side, the system becomes

$\displaystyle x+y=164$

$\displaystyle z+y=90$

$\displaystyle z+y+t=184$

Re: Solving systems of equation

Look at equations 2 and 3. Is it not obvious what t is now?

Re: Solving systems of equation

Re: Solving systems of equation

okay so t is equal to 94....

so can i take out the variable t out from the second and third equation and solve the second and third equation like a regular systems of equation?

Re: Solving systems of equation

Well t only appears in the 3rd equation. Using the 1st and 2nd equations I cannot see how you can solve for x, y and z. It seems like you are missing some information.

Re: Solving systems of equation

You will have to solve for two of the remaining variable in terms of the third.

Re: Solving systems of equation

actually there's 3 variables remaining.... this is so hard

Re: Solving systems of equation

Yes, I mention 3 remaining variables. You will have to express 2 of them in terms of the third.

We know $\displaystyle t=94$. So this leaves:

$\displaystyle y=164-x$

$\displaystyle z=90-y=90-(164-x)=x-74$

This is one way to express the solution, can you find another?

1 Attachment(s)

Re: Solving systems of equation

Well this was my original question

Probability and Statistics homework problem question

Example 1: Computers, fine arts, economics - this one requires using system of equations

There are 500 seniors.

210 are enrolled in computers

80 do not need any of the 3

80 are taking only fine arts.

180 are taking fine arts.

36 taking only economics and computers

10 taking only fine arts and computers

220 taking economics

Find:

1.) P(only taking economics)

2.) P(economics and fine arts)

3.) P(taking all 3 classes)

Then this guy gave me this answer

(View the picture to understand how i got the system) So, you have

the system

1) x + 10 + y + 36 = 210

2) 80 + 10 + z + y = 180

3) 36 + z + y + t = 220

4) x + 10 + y + 36 + t + z + 80 = 420

4 Systems, 4 variables, solve

Attachment 25820

Re: Solving systems of equation

Okay, the diagram is correct, but leaves out the 80 not taking any of the 3. The system I get is:

$\displaystyle x+y+z+t=294$

$\displaystyle x+y=164$

$\displaystyle y+z=90$

$\displaystyle y+z+t=184$

Now you have 4 equations and 4 unknowns.