Simultaneous Equation- just cant get it! help

blomkvist

3x + y = 9

x - y = -2
_
2


the x is over the two as in a fraction. cant seem to figure it out with the 2.

sponsoredwalk

[latex]^{3x \ + \ y \ = \ 9}_{ \frac{x}{2} \ - \ y \ = \ - 2} [/latex]

There is a very important idea here, it's the idea of equality.
The idea here is that the "x" and the "y" in both equations will be
the same number in both equation.

There are a lot of ways to solve this but here is just one example.

3x + y = 9

If we solve for y:

y = 9 - 3x

Okay, now this literally means that y is 9 - 3x.

If we look at the second equation

[latex] \frac{x}{2} \ - \ y \ = \ - 2 [/latex]

Well, what is y?

Try playing with it and show us what you get, then we can explain
the other ideas that you're probably reading about in school.
Basically here you can find out what x is equal to by getting rid
of the y for a moment and having the whole thing only using x.

http://www.khanacademy.org/video/solving-systems-by-substitution-1

Watcha few videos in this playlist, if you go own the page you'll see that
you're on the 55th video now, watch up to the 60'th to learn this method.

bnt

Another way to solve this is to equate one of the terms by multiplying equation(s) throughout. If you multiply the 2nd equation by 6 throughout, then both equations can be rejigged as 3x = (part). You then have two parts both equal to 3x, and thus to each other, so you can solve for the other variable.

jeepers101

blomkvist wrote: »

3x + y = 9

x - y = -2
_
2


the x is over the two as in a fraction. cant seem to figure it out with the 2.

I get the impression its the fraction in the second equation that is giving you trouble. There is a very important rule when dealing with equations- 'whatever you do to one side of the equation, you MUST do to the other'

So if you multiply one side by 10, you must multiply the other side by 10 also. If you get the square root of one side, you must get the square root of the other.

So taking your second equation, the one with the X/2. To get rid of the fraction, you must multiply it by its denominator (bottom part of fraction). Here the denominator is 2. So multiplying x/2 by 2 will give you x. The same way multiplying 1/2 by 2 will give you 1. Or multiplying 4/7 by 7 will give you 4.

Back to your equation. So to multiply your fraction by 2, you must multiply the entire left hand side of the equation by 2 (including the y variable). And following the earlier rule, (whatever you do to one side you must do to the other) now you must also multiply the right hand side of the equation by 2.

Your equation becomes

x - 2y = -4

Pherekydes

Another method is to add or subtract the two equations. In this case, adding them eliminates the y.