Question

Solve the given linear system
5x+10y=70
5x+25z=270
10y+25z=300

Answer 1

There are a few ways you can solve this, either by substituion or by straight addition/substraction. I always thought substitutionw as easier to understand, so I'll go with that.

You can simplify the 2nd equation to be x= 54-5z, I assume you can do the algebra there.

Answer 2

If you take that, and apply the same principle to a few others, you can get values for y and z as well. for example, the first equation you can get x= 14-2y

Answer 3

Just do that for a couple of values, solving for x,y,z and z, and then resubstitue htose values back in to different equations when necesary.

Answer 4

Does that make sense?

Answer 5

Cause you're taking some value, finding what it is in other's terms, and just replugging it in

Answer 6

woah..

Answer 7

very confusing at all.. :(

Answer 8

What're you finding confusing? Go ahead and try rearranging some of the equations to get some simpler equations such as y=7-1/2x

Answer 9

That's the first step, should be a simple step, basic algebra getting the variable on one side

Answer 10

uh.. ive never try like this..
i only tried like this.

y=5x-3
y=3x-1

Answer 11

Okay, using that example, you know that y= both of those things right? So they have to equal eachother.

Cause if y=n and y=m, then n must = m, right?

So if you set those equal to each other

5x-3=3x-1

Then just simplify

2x = 2

x =1

You just need to do that, but with bigger numbers and a z thrown in

Answer 12

Does that make sense or no?

Answer 13

but.. what if there are three? could you give me an example?

Answer 14

It's just a lot more tedious work. If you solve both y and z for x, the plug them in to the third equation, then you can get x

For example, if y= 2x and z= 2x and y+z =4

Then you can plug those values in

2x +2x =4

4x=4

x= 1

And then you can use the fact that x =1 to find the original 2, so if y=2x then y=2.

Answer 15

You can do the same with your problem, it just looks like its going to have fractions and/or big numbers and I don't have a calculator or pencil + paper handy, but just follow the same steps

Answer 16

Just solve y and z for x, plug whatever those 2 equations are in to the 3rd, solve for x, and then use that value of x to find the original 2.

Answer 17

thanks :)

Answer 18

No problem. Let me know if you need any more help. You can post what you did and I can double check that you did everything right.

This is just how I do those problems by the way. There are other methods that your teacher may prefer, this is just the one that I think makes the most sense.