SOLUTION: I'm 60 years old and I decided to go back to show and this math is a little hard please please help. Plot the graph of the equations 4x - 6y = 2 and 2x - 3y = 1 and interpret

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Question 170730This question is from textbook Intermediate Algebra
: I'm 60 years old and I decided to go back to show and this math is a little hard please please help.
Plot the graph of the equations 4x - 6y = 2 and 2x - 3y = 1 and interpret the result.

thank you in advance.
 This question is from textbook Intermediate Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:


system%284x-6y=2%2C2x-3y=1%29


In order to graph these equations, we must solve for y first.


Let's graph the first equation:


4x-6y=2 Start with the first equation.


-6y=2-4x Subtract 4x from both sides.


y=%282-4x%29%2F%28-6%29 Divide both sides by -6 to isolate y.


y=%282%2F3%29x-1%2F3 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=%282%2F3%29x-1%2F3.


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Now let's graph the second equation:


2x-3y=1 Start with the second equation.


-3y=1-2x Subtract 2x from both sides.


y=%281-2x%29%2F%28-3%29 Divide both sides by -3 to isolate y.


y=%282%2F3%29x-1%2F3 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=%282%2F3%29x-1%2F3.


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Now let's graph the two equations together:


Graph of y=%282%2F3%29x-1%2F3 (red). Graph of y=%282%2F3%29x-1%2F3 (green)


From the graph, we can see that one line is right on top of the other one, which means that they intersect an infinite number of times.


So there are an infinite number of solutions. This means that the system of equations is consistent and dependent.