SOLUTION: explain Please: if x can be a real number y= EQUATION 1 6x+3y=4 EQUATION 2 4-3y=6x express as an ordered pair(x,____)

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: explain Please: if x can be a real number y= EQUATION 1 6x+3y=4 EQUATION 2 4-3y=6x express as an ordered pair(x,____)       Log On


   

Question 929186: explain Please:
if x can be a real number y=
EQUATION 1
6x+3y=4
EQUATION 2
4-3y=6x
express as an ordered pair(x,____)
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Those are both equivalent equations for the same two dimensional line.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


6x%2B3y=4.....EQUATION 1
4-3y=6x+...EQUATION 2
___________________
6x%2B3y=4.....EQUATION 1
-6x-3y=-4+...EQUATION 2
______________

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



Start with the given system of equations:


6x%2B3y=4

-6x-3y=-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


6x%2B3y=4 Start with the given equation



3y=4-6x Subtract 6+x from both sides



3y=-6x%2B4 Rearrange the equation



y=%28-6x%2B4%29%2F%283%29 Divide both sides by 3



y=%28-6%2F3%29x%2B%284%29%2F%283%29 Break up the fraction



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



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




So let's solve for y on the second equation


-6x-3y=-4 Start with the given equation



-3y=-4%2B6x Add 6+x to both sides



-3y=%2B6x-4 Rearrange the equation



y=%28%2B6x-4%29%2F%28-3%29 Divide both sides by -3



y=%28%2B6%2F-3%29x%2B%28-4%29%2F%28-3%29 Break up the fraction



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





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


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


These are equivalent equations. The lines are actually the same line, and they 'cross' at infinitely many points (every point on the line). If you try to solve this system algebraically, you'll end up with something that's true, such as 0+=+0.