SOLUTION: Solve the following systems of equations for both x and y. 6x + 7y = 80 2x + 5y = 48

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Question 492016: Solve the following systems of equations for both x and y.
6x + 7y = 80
2x + 5y = 48
Answer by MathLover1(20849) 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:


6x%2B7y=80

2x%2B5y=48





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


6x%2B7y=80 Start with the given equation



7y=80-6x Subtract 6+x from both sides



7y=-6x%2B80 Rearrange the equation



y=%28-6x%2B80%29%2F%287%29 Divide both sides by 7



y=%28-6%2F7%29x%2B%2880%29%2F%287%29 Break up the fraction



y=%28-6%2F7%29x%2B80%2F7 Reduce



Now lets graph y=%28-6%2F7%29x%2B80%2F7 (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+%28-6%2F7%29x%2B80%2F7%29+ Graph of y=%28-6%2F7%29x%2B80%2F7




So let's solve for y on the second equation


2x%2B5y=48 Start with the given equation



5y=48-2x Subtract 2+x from both sides



5y=-2x%2B48 Rearrange the equation



y=%28-2x%2B48%29%2F%285%29 Divide both sides by 5



y=%28-2%2F5%29x%2B%2848%29%2F%285%29 Break up the fraction



y=%28-2%2F5%29x%2B48%2F5 Reduce





Now lets add the graph of y=%28-2%2F5%29x%2B48%2F5 to our first plot to get:


Graph of y=%28-6%2F7%29x%2B80%2F7(red) and y=%28-2%2F5%29x%2B48%2F5(green)


From the graph, we can see that the two lines intersect at the point (4,8) (note: you might have to adjust the window to see the intersection)