SOLUTION: x-y=15 x*y=700 what is x and y please show how to solve equation

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Question 210670: x-y=15
x*y=700
what is x and y
please show how to solve equation
Found 2 solutions by algebrapro18, Edwin McCravy:
Answer by algebrapro18(249)   (Show Source): You can put this solution on YOUR website!
This is your standard system of equations with 2 variables and 2 unknowns. Its a little different because you will end up having to solve a quadratic equation but otherwise you solve it just like any other system. I would solve this system using substitution.

First solve the first equation for x by adding y to both sides

x-y = 15
x = 15+y

Next substitute that into the second equation and solve for y.

xy = 700
(15+y)(y) = 700
15y+y^2 = 700
y^2+15y-700=0

Now we need to find factors of -700 that add to 15.

so the factors of -700 are:
-1, 700
-2, 350
-5, 45
-7, 100
-10, 70
-14, 50
-20, 35

And -20+35 = 15 so thats the pair we need

so y^2+15y-700=0 factors into
(x-20)(x+35)=0
now by the zero product property we split those into two equations and solve and get x = 20 and x = -35.

Next we substitute both solutions into the modified equation one.

x = 15 + y or x = 15 + y
x = 15 + 20 or x = 15 + -35
x = 35 or x = -20

so your solutions would be (35,20) or (-20,-35).
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!


Solve the first equation for x:




Substitute  for  in the equation 




Turn the multiplication around on the left side
(Not really necessary)



Distribute on the left side



Get 0 on the right by subtracting 700 from both sides:



Get the left side in descending order of exponents of 



Factor:



Set each factor equal to 0:

 gives 

 gives 

To find  when , substitute 
for  in 





So that's one solution: 

To find  when , substitute 
for  in 





So the other solution is: 

Edwin
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