SOLUTION: Twice the square of the first number minus the second number is -3. The square of the sum of the first number and 5 is equal to the second number minus 2. Please include "let st

Algebra ->  Equations -> SOLUTION: Twice the square of the first number minus the second number is -3. The square of the sum of the first number and 5 is equal to the second number minus 2. Please include "let st      Log On


   

Question 1100221: Twice the square of the first number minus the second number is -3. The square of the sum of the first number and 5 is equal to the second number minus 2.
Please include "let statements" and equations. Thank you!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = 1st number
Let +b+ = 2nd number
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(1) +2a%5E2+-+b+=+-3+
(2) +%28+a+%2B+5+%29%5E2+=+b+-+2+
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(1) +b+=+2a%5E2+%2B+3+
Plug (1) into (2)
(2) +%28+a+%2B+5+%29%5E2+=+2a%5E2+%2B+3+-+2+
(2) +a%5E2+%2B+10a+%2B+25+=+2a%5E2+%2B+1+
(2) +a%5E2+-+10a+-+24+=+0+
(2) +%28+a+-+12+%29%2A%28+a+%2B+2+%29+=+0+ ( by looking at it )
+a+=+12+
+a+=+-2+
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(1) +2%2A%28-2%29%5E2+-+b+=+-3+
(1) +2%2A4+-+b+=+-3+
(1) +8+-+b+=+-3+
(1) +b+=+11+
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also:
(1) +2%2A%2812%29%5E2+-+b+=+-3+
(1) +288+-+b+=+-3+
(1) +b+=+291+
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check:
(2) +%28+a%2B5+%29%5E2+=+b+-+2+
(2) +%28+-2%2B5+%29%5E2+=+11+-+2+
(2) +3%5E2+=+11+-+2+
(2) +9+=+9+
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(2) +%28+12%2B+5+%29%5E2+=+291+-+2+
(2) +289+=+291+-+2+
(2) +289+=+289+
OK
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There are 2 pairs of solutions:
+a+=+-2+
+b+=+11+
and
+a+=+12+
+b+=+291+
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check the math & get another opinion if needed