I need Algebra help. I need to solve the following equations.......?

Question

y=-2x (plus) 9

-y=x-8

y=3x (plus) 2

-y=2x-3

I need to show work, and I am oblivious as to how to work these problems. Please help.

Answer 1

Each of those equations has an infinite number of solutions.  They are called "linear equations" because if you were to graph the solution set on a Cartesian coordinate plane, you'd get a straight line.

I'm afraid you're going to have to be a bit more specific as to what you mean by "solve the following equations".  Do you need to solve them for x?  Do you need to provide a few ordered pairs that solve them?  Do you need to graph them?

Edit:  I'm sorry, honey.  "The opposite equation"?  I have no idea what that means.  If these problems are coming out of a textbook, could you type the instructions for the problems exactly as they appear there?  That might help clear up the confusion.

Answer 2

Okay, simultaneous equations; you basically solve these by substituing either x or y in one equation from another...

For example if you take your first two equations (and tidy them up a little so they read better):

1: y = 9 - 2x

2: y = 8 - x

Then you could make the first one read:

1: 8 - x = 9 - 2x

by simply substituing 8 - x for y as they are equal (the second equation tells you you this).

Then pull the "x"s and the numbers to different sides and you get:

-x + 2x = 9 - 8

which simplifies to

x = 1

and you can then put this into your second equation to get:

y = 8 - 1

and this simplifies to:

y = 7

so the answer to the first pair is:

x = 1, y = 7

which can be confirmed by putting these values into the two equations:

7 = 9 - 2

7 = 8 - 1

I am guessing you have mistyped the second set as the answers for this set are:

x = 1/5, y = 13/5

and this seems a little unlikely if the first one gave integer results...

Answer 3

Sorry, but when you have two variables, you need two equations, in order to "solve" for both variables.  In the cases you presented, if the question asked you to "solve" for X, you could express each equation in terms of "y" but you can't solve to get a specific number value.

For instance:

y = -2x + 9  or

y - 9 = -2x  or

9 - y = 2x   so  x = (9 -y) / 2