Question 230203
graph each equation to find the solution
x-2y=4
x=2y


Step 1.  To plot the line you need two point:


Step 2.  Let's start with x-2y=4.


Let x=0, then 0-2y=4 and y=-2.  So one point is (0,2)


Let y=0, then x-2*0=4 or x=4.   So the other points (-2,4).


We will use these points to graph the line.


Step 3.  Let's now work with x=2y.


Let x=0, then 2*0=y or y=0.  So one point is (0,0)


Let x=1, then 2*1=y or y=2.  So another point is (1,2)


We will use these points to graph the line.


Step 4.  The graphs are shown below:


{{{graph(400,400,-10,10, -10,10, x/2-2,x/2)}}}


We note that the lines are parallel and have the same slope.  The two equations are given in slope-intercept form where y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b) are shown below


{{{y=x/2-2}}}  


{{{y=x/2}}}


For this example we see both lines have a slope {{{m=1/2}}} and different y-intercepts.  One line has a y-intercept of -2 and the other line has a y-intercept of 0.


Step 5.  ANSWER: Since the lines are parallel and do not intersect, there are NO SOLUTIONS to this problem.


I hope the above steps were helpful.


For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


Good luck in your studies!


Respectfully,
Dr J