Question 579183:
I could really use some help with this one... it's left me stumped...
Solve each system graphically. Be sure to check your solution. If the system has an infinite number of solutions, use set−builder notation to write the solution set. If the system has no solution, state this.
2x − 3y = 6, 3y − 2x = −6
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! You are expected to graph the two equations and see if they have many, one, or no points in common. The point in common would be the solution. When you solve graphically, if it seems like the graph of the equations have a certain point in common, you are expected to verify that what looks like actually is. You do that by substituting the coordinates of that point in both equations, and seeing that the coordinates satisfy both equations.
The equations are linear equations, that graph as straight lines. To graph each line, you just need to plot two points from the line, and connect them with a straight line. To find the coordinates of a point in the graph of a function, you set a value for one variable and find the value for the other. With skill and some luck, you can find a couple of points that will be easy to calculate, easy to plot, and that will make drawing the line easy.
Setting a variable to zero often works well.
For  :
x=0 results in  -->  -->  -->  , giving you point (0,-2).
y=0 results in  -->  -->  -->  , giving you point (3,0).
Now you can plot those points, and connect them with a line to get the graph of  .
For  , you could do the same, and you would find points (0,-2) and (3,0). Those are the same points found for the other line. Both equations represent the same line. If you multiply both sides of the equal sign times the same non-zero number, you get an equivalent equation. You can make an infinite number of them. In fact you can go from one equation to the other by multiplying both sides of the equal sign times (-1).
Since both equations represent the same line, all points in the line are solutions.
So you are expected to state the set of solutions as
{(x,y):2x-3y=6}, or some such thing.
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