SOLUTION: Plot the graph of the equations and interpret the result. 1. 3x - 8y = 5 4x - 2y = 11 2. 4x - 6y = 2 2x - 3y = 1 3. 10x - 4y = 3 5x - 2y = 2

Algebra ->  Graphs -> SOLUTION: Plot the graph of the equations and interpret the result. 1. 3x - 8y = 5 4x - 2y = 11 2. 4x - 6y = 2 2x - 3y = 1 3. 10x - 4y = 3 5x - 2y = 2       Log On


   

Question 153292: Plot the graph of the equations and interpret the result.
1. 3x - 8y = 5
4x - 2y = 11
2. 4x - 6y = 2
2x - 3y = 1
3. 10x - 4y = 3
5x - 2y = 2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you started

# 1



Start with the given system of equations:


system%283x-8y=5%2C4x-2y=11%29


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


Let's graph the first equation:


3x-8y=5 Start with the first equation.


-8y=5-3x Subtract 3x from both sides.


y=%285-3x%29%2F%28-8%29 Divide both sides by -8 to isolate y.


y=%283%2F8%29x-5%2F8 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=%283%2F8%29x-5%2F8.


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


Now let's graph the second equation:


4x-2y=11 Start with the second equation.


-2y=11-4x Subtract 4x from both sides.


y=%2811-4x%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=2x-11%2F2 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=2x-11%2F2.


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


Now let's graph the two equations together:


Graph of y=%283%2F8%29x-5%2F8 (red). Graph of y=2x-11%2F2 (green)


From the graph, we can see that the two lines intersect at the point . So the solution to the system of equations is . This tells us that the system of equations is consistent and independent.




# 2



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.


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


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.


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


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.