Question 1117902: I'm thinking of two numbers.The first plus twice the second equals 11.Twice the first plus three times the second equals 50. Can these be token for for me.
Answer by greenestamps(13216)   (Show Source):
You can put this solution on YOUR website!
By informal logical reasoning....
(1) first plus twice the second is 11
(2) twice the first plus three times the second is 50
(3) comparing (1) and (2), the first plus the second is 39
(4) comparing (1) and (3), the second is -28
(5) from (3) and (4), the first is 67
Answer: 67 and -28
We could solve the problem exactly the same way using formal algebra:
(1) x+2y = 11
(2) 2x+3y = 50
(3) subtracting (1) from (2), x+y = 39
(4) subtracting (3) from (1), y = -28
(5) subtracting (4) from (3), x = 67
However, the methods of algebra allow us to be more efficient in finding the solution:
(1) x+2y = 11
(2) 2x+3y = 50
(3) multiplying (1) times 2, 2x+4y = 22
(4) subtracting (2) from 3, y = -28
(5) substituting y=-28 in (1), x = 67
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