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### Simultaneous Equations

```
Date: Fri, 18 Nov 1994 07:58:28 -0800
From: (Paul Pragin)
Subject: dr.math

Hi.  My name is Paul. How do you do this?

2y+10x=180
4x+4y=100

Please explain how you do this system.
```

```
Date: Fri, 18 Nov 1994 11:48:19 +0000
From: Elizabeth Anna Weber
Subject: Re: dr.math

Hi Paul!  Thanks for writing to Dr. Math.

To solve a system of equations, first solve for one variable.

4x+4y=100, so

4x=100-4y, and we have

x=25-y

Now that we know something about x, let's see if we can use this
to find out some more about y.

2y+10x=180, and we can substitute something for x, now

2y+10(25-y)=180, so

2y+250-10y=180.  Combining a few terms, we have

-8y=-70, so

y=70/8

Remember, we said x=25-y

So, x=25-(70/8)

x=200/8-70/8

x=130/8

If we go back to our original equations, we can check that this works:

4x+4y=100

4(130/8)+4(70/8)=100

130/2+70/2=100

200/2=100

100=100

Now, can you solve these systems?

4y+6x=80            8x+3y=120

3y+4x=60            9x+2y=150

--Elizabeth Weber, doctor on call
```
Associated Topics:
Middle School Equations

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