SOLUTION: 3y − x = −16 2x − 5y = 25 Please solve the system of equations.

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Question 912114: 3y − x = −16
2x − 5y = 25
Please solve the system of equations.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

3y-x%09+=+-16
2x-5y=+25
_____________________________

-x%2B%093y+=+-16
2x-5y=+25


Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


-x%2B3y=-16

2x-5y=25





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


-x%2B3y=-16 Start with the given equation



3y=-16%2Bx Add +x to both sides



3y=%2Bx-16 Rearrange the equation



y=%28%2Bx-16%29%2F%283%29 Divide both sides by 3



y=%28%2B1%2F3%29x%2B%28-16%29%2F%283%29 Break up the fraction



y=%281%2F3%29x-16%2F3 Reduce



Now lets graph y=%281%2F3%29x-16%2F3 (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+%281%2F3%29x-16%2F3%29+ Graph of y=%281%2F3%29x-16%2F3




So let's solve for y on the second equation


2x-5y=25 Start with the given equation



-5y=25-2x Subtract 2+x from both sides



-5y=-2x%2B25 Rearrange the equation



y=%28-2x%2B25%29%2F%28-5%29 Divide both sides by -5



y=%28-2%2F-5%29x%2B%2825%29%2F%28-5%29 Break up the fraction



y=%282%2F5%29x-5 Reduce





Now lets add the graph of y=%282%2F5%29x-5 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F3%29x-16%2F3%2C%282%2F5%29x-5%29+ Graph of y=%281%2F3%29x-16%2F3(red) and y=%282%2F5%29x-5(green)


From the graph, we can see that the two lines intersect at the point (-5,-7) (note: you might have to adjust the window to see the intersection)