SOLUTION: Please help me get started solving this equation: 4/3x + 2y = 6 I know you need to get a common denominator but I am not sure how this works with a fraction like 4/3x involve

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Question 282696: Please help me get started solving this equation:
4/3x + 2y = 6
I know you need to get a common denominator but I am not sure how this works with a fraction like 4/3x involved....
Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
Sorry there is not one unique solution.
This is one equation with two variables (unknowns).
To solve we need one equation for each unknown.
To solve an equation means to find the value of the variables.
Now it appears that you don't really want to solve the equations but you want to know if the lines are parallel or perpendicular or neither.
What is the full original problem as given by the teacher or the book?
1/2x - y/3 = 2
4/3x + 2y = 6
They are not parallel. They do cross at x = 13/54, y = 3/13
Now the question is whether they are perpendicular.
For that we do need the slopes
we can find the slope when the equation is in the form y=mx+b
or while it is the standard form ax+by+c=0
They are both in standard form
first a=1/2 and b=-1/3
-a/b
-1/2/-1/3=-1/2*-3=3/2=slope
second
a=4/3 and b=2
-a/b=
-4/3/2=-4/3*1/2=-2/3 =slope
-2/3*3/2=-1
They are perpendicular since the product of the slopes is -1.