SOLUTION: The difference between the squares of two numbers is 84. Twice the square of the second number subtracted from the square of the first number is 68. Find the numbers What I have

Algebra ->  Systems-of-equations -> SOLUTION: The difference between the squares of two numbers is 84. Twice the square of the second number subtracted from the square of the first number is 68. Find the numbers What I have      Log On


   

Question 818722: The difference between the squares of two numbers is 84. Twice the square of the second number subtracted from the square of the first number is 68. Find the numbers
What I have:
x^2 - y^2 = 84
2y^2 - x^2 = 68 ?????
Found 2 solutions by jhunjiro, MathTherapy:
Answer by jhunjiro(67) About Me  (Show Source):
You can put this solution on YOUR website!
Let:
x=1st number
y=2nd number
1st eq. x^2 - y^2 = 84
2nd eq. x^2 -2y^2= 68
Solution:
x%5E2+-+y%5E2+=+84++
+x%5E2=84%2By%5E2
Substitution:
+%2884%2By%5E2%29-2y%5E2=68
+y%5E2-2y%5E2=68-84
+-y%5E2=-16 = +y%5E2=16
+sqrt+%28y%5E2%29=sqrt+%2816%29
+y=4
+x%5E2+-%284%29%5E2=84
+x%5E2+-+16=84
+x%5E2=100
sqrt+%28x%5E2%29=+sqrt+%28100%29+
+x=10
FINAL ANSWER:
+y=4
+x=10










Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

The difference between the squares of two numbers is 84. Twice the square of the second number subtracted from the square of the first number is 68. Find the numbers
What I have:
x^2 - y^2 = 84
2y^2 - x^2 = 68 ?????

That's INCORRECT!!


You have the 1st number as x, so 2nd number is y

It should then be: 

x%5E2+-+y%5E2+=+84, and 

x%5E2+-+2y%5E2+=+68

Solve this system and you should end up with first number: highlight_green%2810%29, and second number: highlight_green%284%29

You can do the check!! 



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