SOLUTION: I need some help with this problem: 4/3x+3/2y=-4/3 -16/9x-2y=16/9 I'm using the addition/elimination method. I just don't know what to multiply to the top equation to make o

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: I need some help with this problem: 4/3x+3/2y=-4/3 -16/9x-2y=16/9 I'm using the addition/elimination method. I just don't know what to multiply to the top equation to make o      Log On


   

Question 998985: I need some help with this problem:
4/3x+3/2y=-4/3
-16/9x-2y=16/9
I'm using the addition/elimination method.
I just don't know what to multiply to the top equation
to make one of the variables cancel out. please help me.
Found 2 solutions by ikleyn, KMST:
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
(4/3)x   + (3/2)y = -4/3,
(-16/9)x -     2y = 16/9.

Multiply the first equation by  4%2F3  (both sides). You will get 

 %2816%2F9%29x + 2y = -16%2F9
%28-16%2F9%29x - 2y =  16%2F9

Now add both equations. You will get

0*x + 0*y = 0.

In this way you excluded x. But you excluded y in the same time, too.

It is because your original system is dependent: the equations are proportional, and the right sides are proportional with the same coefficient of proportionality.

As a result, your system has infinitely many solution.

You can assign any value to x and then to determine an appropriate value of y from, let say, the first equation of your original system. 
Then this pair of values (x,y) will be the solution of the second equation, too.

Is it clear to you?

If you have question, you can put it into the "Student comment" section. 
Do not forget to point the number of this problem (# 998985) in order I could identify it.

Good luck.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I assume your system is
system%28%284%2F3%29x%2B%283%2F2%29y=-4%2F3%2C-%2816%2F9%29x-2y=16%2F9%29
There are fractions in those equations, and they make mistakes more probable, so I would get rid of them first.
To get rid of fractions in an equation, we can multiply both sides of the equal sign times a multiple of all the denominators to get an equivalent equation.
Shown baby step, by baby step, it looks like this:
%284%2F3%29x%2B%283%2F2%29y=-4%2F3-->6%2A%28%284%2F3%29x%2B%283%2F2%29y%29=6%2A%28-4%2F3%29-->6%2A%284%2F3%29x%2B6%2A%283%2F2%29y=-8%29-->8x%2B9y=-8%29 .
Working with the other equation in a similar way we get to a much nicer system.
system%28%284%2F3%29x%2B%283%2F2%29y=-4%2F3%2C-%2816%2F9%29x-2y=16%2F9%29--->system%288x%2B9y=-8%2C-16x-18y=16%29 .
The equation -16x-18y=16 can be simplified by
dividing both sides of the equal sign by 2:
-16x-18y=16-->-16x%2F2-18y%2F2=16%2F2-->-8x-9y=8
With that we get an equivalent system that is really user-friendly:
system%28%284%2F3%29x%2B%283%2F2%29y=-4%2F3%2C-%2816%2F9%29x-2y=16%2F9%29--->system%288x%2B9y=-8%2C-16x-18y=16%29--->system%288x%2B9y=-8%2C-8x-9y=8%29 .
Now you realized that the second equation is the first equation multiplied times -1 .
They are equivalent equation that would graph as the same line.
There are infinite solutions: all the points on that line.
The system is dependent.