Question 987802
.
Solve the system of equations 


{{{system(x + y = 2,
x^2 + 2y^2 = 11)}}}.
-----------------------------


Express x from the first equation  x = 2-y  and substitute it into the second equation.  You will get


{{{(2-y)^2}}} + {{{2y^2}}} = {{{11}}},


{{{4 - 4y + y^2}}} + {{{2y^2}}} - {{{11}}} = 0,


{{{3y^2 - 4y - 7}}} = {{{0}}},


{{{y[1,2]}}} = {{{(4 +- sqrt (4^2 + 4*3*7))/6}}} = {{{(4 +- sqrt (16 + 84))/6}}} = {{{(4 +- sqrt (100))/6}}} = {{{(4 +- 10)/6}}}.


{{{y[1]}}} = {{{(4 + 10)/6}}} = {{{14/6}}} = {{{2}}}{{{1/3}}};


{{{y[1]}}} = {{{(4 - 10)/6}}} = {{{(-6)/10}}} = -1.