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  -> Lessons  -> Linear Equations Lesson -> 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 1130557: 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.)

2x − 3y = 6
y = 2/3x + 5


Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
2x+-3y+=+6
y+=+%282%2F3%29x+%2B+5+
standard form:
2x+-3y+=+6
-%282%2F3%29x%2B+y+=++5+

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


Let's look at the second equation %28-2%2F3%29x%2By=5


3%28%28-2%2F3%29x%2By%29=3%285%29 Multiply both sides of the second equation by the LCD 3



-2x%2B3y=5 Distribute



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So our new system of equations is:


2x-3y=6

-2x%2B3y=5





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


2x-3y=6 Start with the given equation



-3y=6-2x Subtract 2+x from both sides



-3y=-2x%2B6 Rearrange the equation



y=%28-2x%2B6%29%2F%28-3%29 Divide both sides by -3



y=%28-2%2F-3%29x%2B%286%29%2F%28-3%29 Break up the fraction



y=%282%2F3%29x-2 Reduce



Now lets graph y=%282%2F3%29x-2 (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+%282%2F3%29x-2%29+ Graph of y=%282%2F3%29x-2




So let's solve for y on the second equation


-2x%2B3y=5 Start with the given equation



3y=5%2B2x Add 2+x to both sides



3y=%2B2x%2B5 Rearrange the equation



y=%28%2B2x%2B5%29%2F%283%29 Divide both sides by 3



y=%28%2B2%2F3%29x%2B%285%29%2F%283%29 Break up the fraction



y=%282%2F3%29x%2B5%2F3 Reduce





Now lets add the graph of y=%282%2F3%29x%2B5%2F3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%282%2F3%29x-2%2C%282%2F3%29x%2B5%2F3%29+ Graph of y=%282%2F3%29x-2(red) and y=%282%2F3%29x%2B5%2F3(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.