SOLUTION: Please help me solve each system by equation and graphing. 3x - 5y = -9 5x - 6y = -8 Respectfully yours

Algebra ->  Linear-equations -> SOLUTION: Please help me solve each system by equation and graphing. 3x - 5y = -9 5x - 6y = -8 Respectfully yours      Log On


   

Question 365707: Please help me solve each system by equation and graphing.
3x - 5y = -9
5x - 6y = -8
Respectfully yours
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


3x-5y=-9

5x-6y=-8





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


3x-5y=-9 Start with the given equation



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



-5y=-3x-9 Rearrange the equation



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



y=%28-3%2F-5%29x%2B%28-9%29%2F%28-5%29 Break up the fraction



y=%283%2F5%29x%2B9%2F5 Reduce



Now lets graph y=%283%2F5%29x%2B9%2F5 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%283%2F5%29x%2B9%2F5%29+ Graph of y=%283%2F5%29x%2B9%2F5




So let's solve for y on the second equation


5x-6y=-8 Start with the given equation



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



-6y=-5x-8 Rearrange the equation



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



y=%28-5%2F-6%29x%2B%28-8%29%2F%28-6%29 Break up the fraction



y=%285%2F6%29x%2B4%2F3 Reduce





Now lets add the graph of y=%285%2F6%29x%2B4%2F3 to our first plot to get:


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


From the graph, we can see that the two lines intersect at the point (2,3) (note: you might have to adjust the window to see the intersection)




Because the two lines intersect at the point (2,3), this means that x=2 and y=3