SOLUTION: Solve the system by graphing. Give the answer as a general ordered pair. (Simplify your answer completely.) 2x = 3(4 − y) 3y = 2(6 − x)

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve the system by graphing. Give the answer as a general ordered pair. (Simplify your answer completely.) 2x = 3(4 − y) 3y = 2(6 − x)       Log On


   

Question 1130555: Solve the system by graphing. Give the answer as a general ordered pair. (Simplify your answer completely.)

2x = 3(4 − y)
3y = 2(6 − x)
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
rewrite as 2x=12-3y or 2x+3y=12
and 3y=12-2x, so 2x+3y=12
Infinite solutions of the form y=-(2/3)x+4
so if x is 3 y is 2
(0, 4) is an example as is (6, 0)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
2x+=+3%284+-+y%29
3y+=+2%286+-x%29
standard form:
2x+=+12+-+3y
3y+=+12+-2x
------------------
2x+%2B3y=+12+
2x%2B3y+=+12
------------------as you can see it's same line

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



Start with the given system of equations:


2x%2B3y=12

2x%2B3y=12





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%2B3y=12 Start with the given equation



3y=12-2x Subtract 2+x from both sides



3y=-2x%2B12 Rearrange the equation



y=%28-2x%2B12%29%2F%283%29 Divide both sides by 3



y=%28-2%2F3%29x%2B%2812%29%2F%283%29 Break up the fraction



y=%28-2%2F3%29x%2B4 Reduce



Now lets graph y=%28-2%2F3%29x%2B4 (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+%28-2%2F3%29x%2B4%29+ Graph of y=%28-2%2F3%29x%2B4




So let's solve for y on the second equation


2x%2B3y=12 Start with the given equation



3y=12-2x Subtract 2+x from both sides



3y=-2x%2B12 Rearrange the equation



y=%28-2x%2B12%29%2F%283%29 Divide both sides by 3



y=%28-2%2F3%29x%2B%2812%29%2F%283%29 Break up the fraction



y=%28-2%2F3%29x%2B4 Reduce





Now lets add the graph of y=%28-2%2F3%29x%2B4 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-2%2F3%29x%2B4%2C%28-2%2F3%29x%2B4%29+ Graph of y=%28-2%2F3%29x%2B4(red) and y=%28-2%2F3%29x%2B4(green)


From the graph, we can see that the two lines are identical (one lies perfectly on top of the other) and intersect at all points of both lines. So there are an infinite number of solutions and the system is dependent.