Question

1) (x^2+6xy+y^2=16 x-3y=-2 2) 2x+5xy=14 y-5xy=-9

Answer 1

1)
$x-3y=-2\Rightarrow x=3y-2\\x^2+6xy+y^2=16\\9y^2-12y+4+18y^2-12y+y^2=16\\28y^2-24y-12=0\\7y^2-6y-3=0\\D=36+84=120=(4\sqrt{30})^2\\y_1={3-\sqrt{30}\over7}\Rightarrow x_1={-5-3\sqrt{30}\over7}\\y_2={3+\sqrt{30}\over7}\Rightarrow x_2={3\sqrt{30}-5\over7}$

2)
$2x+5xy=14\\y-5xy=-9\\(2x+5xy)+(y-5xy)=14-9\\2x+y=5\\y=5-2x\\2x+25x-10x^2=14\\10x^2-27x+14=0\\D=13^2\\x_1={27-13\over20}={7\over10}\Rightarrow y_1= {18\over5}\\\\x_2={27+13\over20}=2 \Rightarrow y_2=1$