SOLUTION: Solve each of the following systems by graphing. 2x – y = 4 2x –y = 6 Solve each of the following systems by graphing. X –2y = 8 3x –2y = 12 Solve each of the following s

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1. 2x – y = 4
2x –y = 6

ANSWER:
FIRST OF ALL REWRITE THESE EQUATIONS IN TERMS OF X,

==> 2x – 4 = y
2x –6 = y

Now give arbitrary values for x and find corresponding values of y.

Using these values plot the graph for these two equations.

Then the graph comes like this.









Since two graphs are parellel, these two equations have no solution.



2. X –2y = 8

3x –2y = 12

Follow the same procedure as above,

we have equations,


y = x/2 -4 and

y = (3/2)x - 6


Now find out values of y corresponding the values of x.

Using these values plot the graph...


Then the graph comes like this,








Here two lines intersect at a point. Draw lines perpendicular to x axis and y axis.
At X axis we have the point 2 and on the Y axis we have -3
So solution for these equations is ( 2, -3)



3. 3x –6y = 9

X –2y = 3


Here equations become,

y = (1/2)x - 3/2 and

y =(x/2) - (3/2)

Find out values of x and y and plot the graph.

Then the graph cpmes like this,






Here we can see that both the lines overlap each other,
that means two equations represent the same line.



Hope you Understood.


Regards.

praseenakos@yahoo.co.in