SOLUTION: what does an answer "no solution" mean graphically?

Question 82478: what does an answer "no solution" mean graphically?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Say we had the system of equations

Lets solve the system of equations

Solved by pluggable solver: Solving a linear system of equations by subsitution

Lets start with the given system of linear equations

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y.

Solve for y for the first equation

Subtract from both sides

Divide both sides by 5.

Which breaks down and reduces to

Now we've fully isolated y

Since y equals we can substitute the expression into y of the 2nd equation. This will eliminate y so we can solve for x.

Replace y with . Since this eliminates y, we can now solve for x.

Distribute 10 to

Multiply

Reduce any fractions

Subtract from both sides

Combine the terms on the right side

Now combine the terms on the left side.
Since this expression is not true, we have an inconsistency.

So there are no solutions. The simple reason is the 2 equations represent 2 parallel lines that will never intersect. Since no intersections occur, no solutions exist.

graph of (red) and (green) (hint: you may have to solve for y to graph these)

and we can see that the two equations are parallel and will never intersect. So this system is inconsistent

RELATED QUESTIONS
Does the systems {2x=5y=6 have a unique solution, no solution or many... (answered by checkley71)

What does it mean, both algebraically and graphically, when an ordered pair (x,y) is a... (answered by Earlsdon,vleith)

What does it mean if your solution is a complex number? Explain what a complex solution... (answered by richard1234)

Solve the system:

-x + 2y - 6z = 4
 x +  y + 2z = 3
2x + 3y + 2z = 5

What... (answered by Edwin McCravy)
When solving a quadratic equation you have 0,1,2 solutions. What does this mean... (answered by Edwin McCravy)
what does the solution of a system of linear equations represent?
how can you tell... (answered by stanbon)
what does it mean for an ordered pair to be a solution to an equation  (answered by josgarithmetic)
If a system has an infinite number of solutions.  Use set-builder notation to write the... (answered by lynnlo)
what does this h(3), mean. I have no... (answered by jim_thompson5910)