SOLUTION: Solve the following for x and y: x - 2y = 15 3x - y = 5

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Question 946935: Solve the following for x and y:
x - 2y = 15
3x - y = 5
Answer by MathLover1(20850) 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:


1x-2y=15

3x-y=5





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


1x-2y=15 Start with the given equation



-2y=15-x Subtract +x from both sides



-2y=-x%2B15 Rearrange the equation



y=%28-x%2B15%29%2F%28-2%29 Divide both sides by -2



y=%28-1%2F-2%29x%2B%2815%29%2F%28-2%29 Break up the fraction



y=%281%2F2%29x-15%2F2 Reduce



Now lets graph y=%281%2F2%29x-15%2F2 (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%2F2%29x-15%2F2%29+ Graph of y=%281%2F2%29x-15%2F2




So let's solve for y on the second equation


3x-y=5 Start with the given equation



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



-y=-3x%2B5 Rearrange the equation



y=%28-3x%2B5%29%2F%28-1%29 Divide both sides by -1



y=%28-3%2F-1%29x%2B%285%29%2F%28-1%29 Break up the fraction



y=3x-5 Reduce





Now lets add the graph of y=3x-5 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F2%29x-15%2F2%2C3x-5%29+ Graph of y=%281%2F2%29x-15%2F2(red) and y=3x-5(green)


From the graph, we can see that the two lines intersect at the point (-1,-8) (note: you might have to adjust the window to see the intersection)