How do you solve equations with two variables?

Question

I'm in Chapter Eight of McDougal Littell's "Algebra Structure and Method--Book One," and if anyone knows that particular book, please answer! I was told to "get Y on one side of the equation with no coefficients," but I don't have Xs or Ys, and I don't get how to divide out a coefficient if it doesn't divide out! Boy, it sucks being sick for two days...

I'm in the first and second sections of 8-1

Answer 1

That's the book I use when I teach, so if you tell me which section in particular you are working on, I might can help you with that particular group of problems.

Let me show you with a particular example; if you need help with a certain problem you can post it for us.

Solve:

2a+3b = 8
3a - b = 1

Take one equation (let's use the second one), and get one variable (the b, for example) by itself:

3a - b = 1
-b = 1 - 3a (subtract both sides by a)
b = -1 + 3a = 3a - 1 (divide both sides by -1)

so we get b = 3a-1. Substitute this value in the other equation. That is:

2a + 3b = 8
2a + 3(3a-1) = 8 (substitute 3a-1 for b)
2a + 9a -3 = 8 (distribute)
11a - 3 = 8 (combine like terms)
11a = 11 (subtract 3 from both sides)
a = 1 (divide both sides by 11)

Then use this to find the other variable:

b = 3a -1 = 3(1) - 1 = 2

So the solution is a=1, b=2, for this example.

There are other methods, but this is the simplest, when it works out evenly.

Answer 2

I don't have the book, but i can walk you through the principles of two variable equations. Your variables can be a and b or x and y or whatever, the principle remains the same. Two solve two variable equations, you need TWO equations. Solve one equation for one variable. For example, if your original equation is: 12x + 2y = 10 then solve for y.

2y = -12x +10
y = -6x + 5

then you can substitute for y in your SECOND EQUATION. So everytime there is a y in your second equation put in what you solved for, the example I gave is (-6x +5).

Hope that helps.

Answer 3

how does the equation look like ? if it has no variables, then it is not a function. you can't divide coefficients, if you meant to get them on the otherside, you have to do the inverse.

Answer 4

the equations don't have to use just X's and Y's. Sometimes they use a's and b's, or s's and t's, etc. etc.

The same procedure is used no matter how the variables are labeled.