SOLUTION: please help I know that I ask for help early but I neddt to see step by step for me to understand I'm 60 years old. thank you so much..... Plot the graph of the equations 10x

Algebra ->  Linear-equations -> SOLUTION: please help I know that I ask for help early but I neddt to see step by step for me to understand I'm 60 years old. thank you so much..... Plot the graph of the equations 10x       Log On


   

Question 170731This question is from textbook
: please help I know that I ask for help early but I neddt to see step by step for me to understand I'm 60 years old. thank you so much.....
Plot the graph of the equations 10x - 4y = 3 and 5x - 2y = 6 and interpret the result.
thank you in advance. really thank you so much. This question is from textbook

Found 2 solutions by jim_thompson5910, stanbon:
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%2810x-4y=3%2C5x-2y=6%29


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


Let's graph the first equation:


10x-4y=3 Start with the first equation.


-4y=3-10x Subtract 10x from both sides.


y=%283-10x%29%2F%28-4%29 Divide both sides by -4 to isolate y.


y=%285%2F2%29x-3%2F4 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=%285%2F2%29x-3%2F4.


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Now let's graph the second equation:


5x-2y=6 Start with the second equation.


-2y=6-5x Subtract 5x from both sides.


y=%286-5x%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=%285%2F2%29x-3 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=%285%2F2%29x-3.


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


Now let's graph the two equations together:


Graph of y=%285%2F2%29x-3%2F4 (red). Graph of y=%285%2F2%29x-3 (green)


From the graph, we can see that the two lines are parallel, which means that they will NEVER intersect.


So there are no solutions. This means that the system of equations is inconsistent.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Plot the graph of the equations 10x - 4y = 3 and 5x - 2y = 6 and interpret the result.
------------------------
10x - 4y = 3
Let x = 0, then y = -3/4; this gives you the point (0,-3/4)---Plot it.
Let y = 0, then x = 3/10; this gives you the point (3/19,0)---Plot it.
Draw the line thru those two points.
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%285%2F2%29x-%283%2F4%29%29
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and 5x - 2y = 6
Let x = 0, then y = -3; this gives you the point (0,-3)---Plot it.
Let y = 0, then x = 6/5; this gives you the point (6/5,0)---Plot it.
Draw the line thru those two points.
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%285%2F2%29x-3%29
--------------------------------
Find the intersection of the two lines; that is the solution
of the system of equations.
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%285%2F2%29x-%283%2F4%29%2C%285%2F2%29x-3%29
Ans: No solution as the lines a parallel.
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Cheers,
Stan H.