Question

1.х^2 - у^2 - 5ху=-6
2. х+у=3

Answer 1

$left { {{x^{2} - y^{2} -5xy=-6} atop {x+y=3}} right. left { {{(3-y)^{2}-y^{2}-5y cdot (3-y) +6=0} atop {x=3-y}} right. \ left { {{{9 -6y+y^{2}-y^{2}-15y+5y^{2}+6=0} atop {x=3-y}} right. left { {{5y^{2}-21y+15=0} atop {x=3-y}} right. \ 5y^{2}-21y+15=0 \ y_{1,2}= frac{21 pm sqrt{441 - 300} }{10}= frac{21 pm sqrt{141} }{10} ; left {{y_{1}=frac{21 + sqrt{141} }{10}} atop {y_{2}=frac{21 - sqrt{141} }{10}}} right.$
$x_{1}=3 - frac{21 + sqrt{141} }{10}}, ; x_{2}=3 - frac{21 - sqrt{141} }{10}}} \ x_{1}= frac{9 - sqrt{141} }{10}}, ; x_{2}=frac{9 + sqrt{141} }{10}}}$