SOLUTION: Solve the system by graphing. (Simplify your answer completely. If the system is dependent, enter a general solution in terms of x and y. If there is no solution, enter NO SOLUTION

Question 1130557: Solve the system by graphing. (Simplify your answer completely. If the system is dependent, enter a general solution in terms of x and y. If there is no solution, enter NO SOLUTION.)

2x − 3y = 6
y = 2/3x + 5

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

standard form:

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

Let's look at the second equation

Multiply both sides of the second equation by the LCD 3

Distribute

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So our new system of equations is:

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 parallel and will never intersect. So there are no solutions and the system is inconsistent.

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