SOLUTION: Solve the following 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 th

Algebra ->  Graphs -> SOLUTION: Solve the following 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 th      Log On


   

Question 1062882: Solve the following 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.
4y=x+4
x=2/3y+8/3
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!


system%284y=x%2B4%2C%0D%0Ax=expr%282%2F3%29y%2B8%2F3%29

Get a table of values for the first equation:

4y=x%2B4     4y=x%2B4      4y=x%2B4
Let x=0     Let y=0     Let y=-1 
4y=0%2B4     4%280%29=x%2B4    4%28-1%29=x%2B4
4y=4       0=x%2B4       -4=x%2B4
y=1        -4=x        -8=x
point (0,1)      point (-4,0)      point (-8,-1) 

Plot those three points and draw a line through them



The other equation contains fractions, so it will be
easier if we first multiply every term in it through by the
LCD of 3:

x=expr%282%2F3%29y%2B8%2F3%29
3x=2y%2B8


3x=2y%2B8     3x=2y%2B8     3x=2y%2B8
Let x=0     Let y=-1     Let x=-2
3%280%29=2y%2B8   3x=2%28-1%29%2B8  3%28-2%29=2y%2B8
0=2y%2B8      3x=-2%2B8     -6=2y%2B8
-8=2y       3x=6        -14=2y
-4=y        x=2         -7=y
point (0,-4)      point (2,-1)      point (-2,-7) 



Now notice the point where the two lines cross. From
that point draw a vertical line directly down to the 
x-axis, and a horizontal line over to the y-axis like 
this:



We see that the vertical line hits the x-axis at 4.
That means x=4 is the answer for x.

We see that the horizontal line hits the y-axis at 2.
That means y=2 is the answer for y.

Solution:  x=4, y=2.

Edwin