Question

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

2) 2x+5xy=14
y-5xy=-9

Answer 1

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

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={27-13over20}={7over10}Rightarrow y_1= {18over5}\\x_2={27+13over20}=2 Rightarrow y_2=1$