SOLUTION: Directions: Solve the system of equations by graphing. {y=3/4x-1 {y=-4/3x-1

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Directions: Solve the system of equations by graphing. {y=3/4x-1 {y=-4/3x-1      Log On


   

Question 902865: Directions: Solve the system of equations by graphing.
{y=3/4x-1
{y=-4/3x-1
Found 2 solutions by richwmiller, MathLover1:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
duplicate or similar problem

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y=%283%2F4%29x-1
y=-%284%2F3%29x-1
_______________________
+-%283%2F4%29x%2By=+-1
%284%2F3%29x%2By=+-1
_____________________________

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


Let's look at the first equation %28-3%2F4%29x%2By=-1



4%28%28-3%2F4%29x%2By%29=4%28-1%29 Multiply both sides of the first equation by the LCD 4



-3x%2B4y=-4 Distribute



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Let's look at the second equation %284%2F3%29x%2By=-1


3%28%284%2F3%29x%2By%29=3%28-1%29 Multiply both sides of the second equation by the LCD 3



4x%2B3y=-4 Distribute



---------




So our new system of equations is:


-3x%2B4y=-4

4x%2B3y=-4





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


-3x%2B4y=-4 Start with the given equation



4y=-4%2B3x Add 3+x to both sides



4y=%2B3x-4 Rearrange the equation



y=%28%2B3x-4%29%2F%284%29 Divide both sides by 4



y=%28%2B3%2F4%29x%2B%28-4%29%2F%284%29 Break up the fraction



y=%283%2F4%29x-1 Reduce



Now lets graph y=%283%2F4%29x-1 (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+%283%2F4%29x-1%29+ Graph of y=%283%2F4%29x-1




So let's solve for y on the second equation


4x%2B3y=-4 Start with the given equation



3y=-4-4x Subtract 4+x from both sides



3y=-4x-4 Rearrange the equation



y=%28-4x-4%29%2F%283%29 Divide both sides by 3



y=%28-4%2F3%29x%2B%28-4%29%2F%283%29 Break up the fraction



y=%28-4%2F3%29x-4%2F3 Reduce





Now lets add the graph of y=%28-4%2F3%29x-4%2F3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%283%2F4%29x-1%2C%28-4%2F3%29x-4%2F3%29+ Graph of y=%283%2F4%29x-1(red) and y=%28-4%2F3%29x-4%2F3(green)


From the graph, we can see that the two lines intersect at the point (-4%2F25,-28%2F25) (note: you might have to adjust the window to see the intersection)