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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
system%28x-y=15%2Cx%2Ay=700%29

Solve the first equation for x:

x-y=15
x=15%2By

Substitute %2815%2By%29 for x in the equation x%2Ay=700%29

x%2Ay=700%29
%2815%2By%29%2Ay=700

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

y%2815%2By%29=700

Distribute on the left side

15y%2By%5E2=700

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

15y%2By%5E2-700=0

Get the left side in descending order of exponents of y

y%5E2%2B15y-700=0

Factor:

%28y%2B35%29%28y-20%29=0

Set each factor equal to 0:

y%2B35=0 gives y=-35

y-20=0 gives y=20

To find x when y=-35, substitute %28-35%29
for y in 

x=15%2By
x=15%2B%28-35%29
x=-20

So that's one solution: %22%28x%2Cy%29%22=%22%28-20%2C-35%29%22

To find x when y=20, substitute %2820%29
for y in 

x=15%2By
x=15%2B%2820%29
x=35

So the other solution is: %22%28x%2Cy%29%22=%22%2835%2C20%29%22

Edwin