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,____)

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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(39618)   (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)   (Show Source): You can put this solution on YOUR website!


.....EQUATION 1
...EQUATION 2
___________________
.....EQUATION 1
...EQUATION 2
______________

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



Start with the given system of equations:










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


Start with the given equation



Subtract from both sides



Rearrange the equation



Divide both sides by



Break up the fraction



Reduce



Now lets graph (note: if you need help with graphing, check out this solver)



Graph of




So let's solve for y on the second equation


Start with the given equation



Add to both sides



Rearrange the equation



Divide both sides by



Break up the fraction



Reduce





Now lets add the graph of to our first plot to get:


Graph of (red) and (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 .

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