SOLUTION: Solve the system by graphing; plotting on the graph 3x-5y=-9 5x-6y=-8 and 4x+5y=-2 4y-x=11

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Question 175918: Solve the system by graphing; plotting on the graph
3x-5y=-9
5x-6y=-8
and
4x+5y=-2
4y-x=11
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started




Start with the given system of equations:


system%283x-5y=-9%2C5x-6y=-8%29


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


Let's graph the first equation:


3x-5y=-9 Start with the first equation.


-5y=-9-3x Subtract 3x from both sides.


y=%28-9-3x%29%2F%28-5%29 Divide both sides by -5 to isolate y.


y=%283%2F5%29x%2B9%2F5 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=%283%2F5%29x%2B9%2F5.


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Now let's graph the second equation:


5x-6y=-8 Start with the second equation.


-6y=-8-5x Subtract 5x from both sides.


y=%28-8-5x%29%2F%28-6%29 Divide both sides by -6 to isolate y.


y=%285%2F6%29x%2B4%2F3 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=%285%2F6%29x%2B4%2F3.


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Now let's graph the two equations together:


Graph of y=%283%2F5%29x%2B9%2F5 (red). Graph of y=%285%2F6%29x%2B4%2F3 (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.