Solving Linear Systems

If x + y = 15 and x - y = -19, then xy= ?????

the easiest way, I find, is to solve through substitution (someone else can kindly explain elimination -- I frankly don't like it).

Isolate one of the equations for either x or y:

x = 15 - y , x - y = -19

Substitute the value into the other equation:

(15 - y) - y = -19

15 - 2y = -19

-2y = -34

y = 17

Now you can substitute the value of y into one of the original equations.

x + 17 = 15

x = -2

and now you have values for both x and y.

Oh, I did it like this:

combine:

x+y=15 and x-y= -19

2x+y-y= -4

Y is cancelled

2x= -4

x= -2


Then I did

-2 +y=15

y=17

I have no idea what that's called...

There's a reason I layed out I Love Link's version like this. In future problems, you'll definately have coefficients with your variables to deal with. In which case, it's good to have the system set up like an addition problem. In order to cancel them out, you'll have to have the variables have equal but opposite coefficients. Like 8x and -8x. You waon't want to just combine the two problems in such a case - this is a bit easier to manage.

So, suppose you had this problem:

4x - y = 19
2x + 2y = 22

You would have to mutliply one equation by an integer to get the x or y to cancel. So, lets do x.

4x + y = 19. -------> 4x + y = 19
-2(2x + 2y = 22) ---> -4x - 4y = -44

From there, you'd just do it like the other problem.

Yeah, that's what I TRIED to do, but it's REALLy hard to on this...

On paper, it's more like how you did it, Tsukasa. Thanks for clarifying it. ^__^

the correct way of typing a linear system is y=kx+m, just so you guys know

i thought it was y=mx+b... or maybe that one's for graphs?

y=mx+b is only slope/ slope intercept form, not for linar equations, Links_mistress.

^Hey man, he was just offering support. He saw that the question was satisfactorily answered, and acquiesced. No need to go picking on him. And would you explain your pointless reference to y + yxb*sq.root 23?

Oh, and I Love Link: what you did was elimination. It works just as well as substitution.

Who said y=mx+b is only for slope is wrong. when there is 2 variables it is sometimes easiest to put them in that form to solve linear equations. You can solve systems of linear equations algebraically, no? Then why can't you use that form?