Question 1043341
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{{{a^2=4b^2}}}
a=1+2b
In the system of equations above, what is the value of a?
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{{{a^2=4b^2}}}   (1)
a=1+2b     (2)

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

{{{(1+2b)^2}}} = {{{4b^2}}}  --->

{{{1 + 4b + 4b^2}}} = {{{4b^2}}}  --->

1 + 4b = 0  --->  b = {{{-1/4}}}.   Then  a ={{{ 1 + 2*(-1/4)}}} = {{{1/2}}}.

<U>Check</U>. {{{a^2}}} = {{{1/4}}}.  {{{4b^2}}} = {{{4*(-1/4)^2}}} = = {{{1/4}}}.

      1 + 2b = {{{1 + 2*(-1/4)}}} = {{{1/2}}}.   {{{1/2}}} = {{{1/2}}}.   !!! Checked !!!

<U>Answer</U>.  a = {{{1/2}}},  b = {{{-1/4}}}.
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