SOLUTION: 2.Plot the graph of the equations 4x-6y=2 and 2x-3y=1 and interpret the results. 4x-6y=2 -4x+6y=-2 0=0 These lines are the same and intersect at every point. Y intercept:

Algebra ->  Graphs -> SOLUTION: 2.Plot the graph of the equations 4x-6y=2 and 2x-3y=1 and interpret the results. 4x-6y=2 -4x+6y=-2 0=0 These lines are the same and intersect at every point. Y intercept:       Log On


   

Question 170807: 2.Plot the graph of the equations 4x-6y=2 and 2x-3y=1 and interpret the results.
4x-6y=2
-4x+6y=-2
0=0
These lines are the same and intersect at every point.
Y intercept:
2x-3y=1
2(0)-3y=1
0-3y/3=1/3 y intercept = (0,1/3)
Y=0: 2x-3(0)=1
2x/2-0=1/2 x intercept = (1/2,0)
4x-6y=2
X=0: 4(0)-6y=2
0-6y/6=2/6 = 1/3 y intercept = (0,1/3)
Y=0: 4x-6(0)=2
4x/4-0=2/4=1/2 x intercept = (1/2,0)
Could you please tell me if I did the above problem correctly and could you show me how to graph it.

3.Plot the graph of the equations 10x-4y=3 and 5x-2y=6
Can you please show me how to do number 3. Thanks Nichole

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


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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.





# 3




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.


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


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.


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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.