SOLUTION: {{{a^2=4b^2}}} a=1+2b In the system of equations above, what is the value of a?

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Question 1043341: a%5E2=4b%5E2
a=1+2b
In the system of equations above, what is the value of a?
Found 3 solutions by t0hierry, ankor@dixie-net.com, ikleyn:
Answer by t0hierry(194) About Me  (Show Source):
You can put this solution on YOUR website!
These two equations look contradictory if you read a = 2b in the first equation. Instead, you have to read a = -2b or 4b = -1 that is b = -1/4 and thus a = 1/2.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a%5E2=4b%5E2
a=1+2b
In the system of equations above, what is the value of a?
this system is inconsistent,
find the the square root of both sides of the first equation.
a = 2b
and the 2nd equation is given as
a = 1 + 2b
obviously not possible

Answer by ikleyn(52782) About Me  (Show Source):
You can put this solution on YOUR website!
.
a%5E2=4b%5E2
a=1+2b
In the system of equations above, what is the value of a?
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a%5E2=4b%5E2   (1)
a=1+2b     (2)

Substitute (2) into (1). You will get

%281%2B2b%29%5E2 = 4b%5E2  --->

1+%2B+4b+%2B+4b%5E2 = 4b%5E2  --->

1 + 4b = 0  --->  b = -1%2F4.   Then  a =+1+%2B+2%2A%28-1%2F4%29 = 1%2F2.

Check. a%5E2 = 1%2F4.  4b%5E2 = 4%2A%28-1%2F4%29%5E2 = = 1%2F4.

      1 + 2b = 1+%2B+2%2A%28-1%2F4%29 = 1%2F2.   1%2F2 = 1%2F2.   !!! Checked !!!

Answer.  a = 1%2F2,  b = -1%2F4.