SOLUTION: Plot the graph of the equations 4x - 6y = 2 and 2x - 3y = 1 and interpret the result. I am having such a difficult time solving this equation. Can someone please help me underst

Question 170422: Plot the graph of the equations 4x - 6y = 2 and 2x - 3y = 1 and interpret the result.
I am having such a difficult time solving this equation. Can someone please help me understand how to do this problem, any help will be greatly appreciated.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Graphing the first equation

In order to graph , we need to solve for "y" first.

Start with the first equation.

Subtract from both sides.

Rearrange the terms.

Divide both sides by to isolate y.

Break up the fraction.

Reduce.

In order to graph this equation, we only need two points to create a straight line

--------------------------------Let's find the first point--------------------------------

Start with the given equation

Plug in

Multiply and to get

Subtract

So when , we have the value . This means we have the first point

--------------------------------Let's find the second point--------------------------------

Start with the given equation

Plug in

Multiply and to get

Subtract

So when , we have the value . This means we have the second point

------------------------------------------------------------------------------------------------

So we have the two points:

and

Now plot these two points on a coordinate system

Now draw a straight line through the two points. This line is the graph of

Graph of through the two points

and

Graphing the second equation

Start with the second equation.

Subtract from both sides.

Rearrange the terms.

Divide both sides by to isolate y.

Break up the fraction.

Reduce.

Take note that this equation is EXACTLY identical to the equation we just plotted. So the graph of (and ) is

Now graphing the two equations together gives you

Note: there are really two equations here. One is just right on top of the other (which hides it)

Since one equation is right on top of the other, this tells us that there are an infinite number of solutions (since there are an infinite number of intersections).

So the system is dependent.

RELATED QUESTIONS
Please help me with this. I am totally confused. Thanks. 1. Plot the graph of the... (answered by stanbon)

2. Plot the graph of the equations 4x - 6y = 2 and 2x - 3y = 1 and interpret the result. (answered by midwood_trail)

Plot the graph of the equations 4x - 6y = 2 and 2x - 3y = 1 and interpret the... (answered by nipunbajaj)

Plot the graph of the equations 3x - 8y = 5 and 4x - 2y = 11 and interpret the result. (answered by checkley77)

Plot the graph of the equations 2x - 3y = 5 and 4x - 6y = 21 and interpret the result. (answered by checkley77)

PLEASE HELP I JUST DON'T UNDERSTAND THESE PROBLEMS AND I DON'T KNOW WHAT TO DO. PLEASE... (answered by ankor@dixie-net.com)

Plot the graph of the equations and interpret the result. 1. 3x - 8y = 5 4x - 2y = (answered by jim_thompson5910)

1. Solve by substitution or elimination method: 3x � 2y = 26 (answered by stanbon)

1. Solve by substitution or elimination method: 3x � 2y = 26 (answered by RAY100)