Question

Решить систему:
а) х-у=1
    1/х+1/у=5/6
б) 4х+ху=6
    3х-5ху=39

Answer 1

$left { {{ x=1+y} atop {1/x+1/y=5/6}} right.$
$frac{1}{1+y} + frac{1}{y} - frac{5}{6} =0$
$frac{6y+6+6y-5y-5y^2}{6y(1+y)} =0$
$-5y^2+7y+6=0; y neq 0;y neq -1$
$5y^2-7y-6=0; y neq 0;y neq -1$
D=49+120=169
y1=2
y2=-3/5
x1=1+y=3
x2=1+y=2/5

$left { {{4x+xy=6} atop { 3x-5xy=39}} right.$
$left { {{20x+5xy=30} atop { 3x-5xy=39}} right.$
$left { {{20x+5xy=30} atop { 23x=69}} right.$
23x=69
x=3
4x+xy=6;  12+3y=6; 3y=-6; y=-2