Question 962719
the system of equations 

{{{y = x^2 + 1}}} ..............eq.1
{{{y = b}}}..............eq.2
-------------------------------
=>since {{{y = x^2 + 1}}} is a parabola with y-intercept at {{{y=1}}} and has two complex solutions ({{{i}}} and {{{-i}}}), 
and your {{{y = b}}} is a horizontal line, then {{{b}}} for which the system of equations has two solutions could be any number greater than {{{1}}}(if {{{b=1}}}, there will be only one solution)  

try {{{b=1}}},{{{b=2}}} and {{{b=5}}}


{{{ graph( 600, 600, -5, 5, -5, 10, x^2 + 1,1,2,5) }}}

so, a value for {{{b}}} for which the system of equations has {{{two}}} solutions are: {{{b}}}={{{2}}},{{{3}}},{{{4}}},........