-2y-16x=12 how do I solve this linear equation?
First you have to know what to expect. Let's review what "solve" means: It means
find numbers that you can put into the equation in place of the variables that will
make the equation a true statement.
There are two variables in this equation, so a "solution" is a pair of numbers ... one
for 'x' and one for 'y' ... that will make the left side equal to 12 .
There are an infinite supply of pairs of numbers that will do that. If you draw a graph of this equation, the graph is a straight line. Every point on the line is a solution to the equation, (and you know how many points there are on a straight line).
So, nobody gave you this equation and told you to "solve" it.
Maybe they told you to " solve it for 'x' ", or maybe " solve it for 'y' ".
I'll show you how to solve it for 'y', because that's the form we usually
want to see if we're getting ready to draw the equation's graph.
-2y - 16x = 12
Divide each side by 2, just to make it a little less complicated :
-y - 8x = 6
Add 8x to each side:
-y = 8x + 6
Multiply each side by -1 :
y = -8x - 6
That's the original equation, just manipulated and massaged
into a different form, but it still says exactly the same thing.
This form is especially useful for graphing. In this form ...
with 'y' all by itself on one side ...
==> The ' -8 ' is the slope of the graph line.
==> The ' -6 ' is where the graph line crosses the y-axis.
With those two pieces of information, you could go right ahead
and draw the graph now, without any more calculating !
[latex]-2y-16x=12 \\ -2y=12+16x \\ y=-6-8x [/latex]
now put various values of x and calculate y and plot them in graph.
Put easy and small values like 0, 1. -1
Only 2 are required to represent them in graph