SOLUTION: how many solutions are for y + 3x = 2 and 2y - 4 = -6x ? one solution, no solution, infinite solutions, cannot be determined

Question 868380: how many solutions are for y + 3x = 2 and 2y - 4 = -6x ?
one solution, no solution, infinite solutions, cannot be determined
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

if you are given this system:
and

___________________________or
and

then,

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

Subtract from 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.

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