SOLUTION: does 3x+7y=8 and 21y=-9x+24 have one solution, no solution or infinitly many solutions

Question 750418: does 3x+7y=8 and 21y=-9x+24 have one solution, no solution or infinitly many solutions

Found 2 solutions by MathLover1, tommyt3rd:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

and

____________________solve the system

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.

Answer by tommyt3rd(5050) (Show Source): You can put this solution on YOUR website!
21y=-9x+24 can be rewritten as 9x+21y=24 and then 3x+7y=8. So it has the same graph (solution) as the first equation. So...many solutions

:)
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