SOLUTION: Solve the system by graphing. (Simplify your answer completely. If the system is dependent, enter a general solution in terms of x and y. If there is no solution, enter NO SOLUTION

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve the system by graphing. (Simplify your answer completely. If the system is dependent, enter a general solution in terms of x and y. If there is no solution, enter NO SOLUTION      Log On


   

Question 1130559: Solve the system by graphing. (Simplify your answer completely. If the system is dependent, enter a general solution in terms of x and y. If there is no solution, enter NO SOLUTION.)

3y + x = 1
y= -1/3x + 1 / 3
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

3y+%2B+x+=+1
y=+-%281%2F3%29x+%2B+1+%2F+3
---------------------------write both equations in standard form

x%2B3y+=+1
%281%2F3%29x+%2By=++1+%2F+3

Solved by pluggable solver: Solve the System of Equations by Graphing


Let's look at the second equation %281%2F3%29x%2By=1%2F3


3%28%281%2F3%29x%2By%29=3%281%2F3%29 Multiply both sides of the second equation by the LCD 3



1x%2B3y=3 Distribute



---------




So our new system of equations is:


1x%2B3y=1

1x%2B3y=3





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


1x%2B3y=1 Start with the given equation



3y=1-x Subtract +x from both sides



3y=-x%2B1 Rearrange the equation



y=%28-x%2B1%29%2F%283%29 Divide both sides by 3



y=%28-1%2F3%29x%2B%281%29%2F%283%29 Break up the fraction



y=%28-1%2F3%29x%2B1%2F3 Reduce



Now lets graph y=%28-1%2F3%29x%2B1%2F3 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F3%29x%2B1%2F3%29+ Graph of y=%28-1%2F3%29x%2B1%2F3




So let's solve for y on the second equation


1x%2B3y=3 Start with the given equation



3y=3-x Subtract +x from both sides



3y=-x%2B3 Rearrange the equation



y=%28-x%2B3%29%2F%283%29 Divide both sides by 3



y=%28-1%2F3%29x%2B%283%29%2F%283%29 Break up the fraction



y=%28-1%2F3%29x%2B1 Reduce





Now lets add the graph of y=%28-1%2F3%29x%2B1 to our first plot to get:


Graph of y=%28-1%2F3%29x%2B1%2F3(red) and y=%28-1%2F3%29x%2B1(green)


From the graph, we can see that the two lines are parallel and will never intersect. So there are no solutions and the system is inconsistent.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Note that the answer from tutor @MathLover1 is incorrect on this one.

The two equations are for the same line, not parallel lines.

See if you can find where in her work she made a simple arithmetic error (like we all make, if we aren't paying attention!) to get her wrong result.

Note that, in practice, the process she went through is FAR more work than is necessary.

The second equation is in slope-intercept form; solve the first equation for y to put it in slope-intercept form, and you will see the two equations are the same.

And note that the previous note also applies to all of the similar questions she has recently answered. The answers to all those problems can be found quickly by putting the two equation either both in standard form (ax+by=c) or both in slope-intercept form.