Решить системы уравнений(где разделить - это дробь)1)x+y=4  5/x-3/y=12)1/x+1/y=7/12   x+y=7

[latex] \left \{ {{x+y=4} \atop { \frac{5}{x} - \frac{3}{y} =1}} \right. [/latex], [latex] \left \{ {{x=4-y} \atop { \frac{5}{4-y} - \frac{3}{y} =1}} \right. [/latex], [latex] \frac{5y-3y+12}{y*(y-4)} =1[/latex], [latex] \frac{2y+12}{y(y-4)} =1[/latex], [latex]2y+12= y^{2} -4y[/latex], [latex] y^{2}-6y-12=0 [/latex], [latex]D=36-4*(-12)=84[/latex], [latex] y_{1} = \frac{6- 2\sqrt{21} }{2} =3- \sqrt{21} [/latex], [latex] y_{2} = \frac{6+2 \sqrt{21} }{2} =3+ \sqrt{21} [/latex], [latex] x_{1} =4-(3- \sqrt{21)} =1+ \sqrt{21} [/latex], [latex] x_{2}=4-(3+ \sqrt{21})=1- \sqrt{21} [/latex]. [latex] \left \{ {{ \frac{1}{x}+ \frac{1}{y}= \frac{7}{12} } \atop {x+y=7}} \right. [/latex], [latex] \left \{ {{ \frac{1}{x}+ \frac{1}{y} = \frac{7}{12} } \atop {x=7-y}} \right. [/latex], [latex] \frac{1}{7-y} + \frac{1}{y} = \frac{7}{12} [/latex], [latex] \frac{y+7-y}{y*(7-y)} = \frac{7}{12} [/latex], [latex] \frac{7}{y*(7-y)} = \frac{7}{12} [/latex], [latex]12=7y- y^{2} [/latex], [latex] y^{2}-7y+12=0 [/latex], [latex]D=49-4*12=1[/latex], [latex] y_{1} = \frac{7-1}{2} =3[/latex], [latex] y_{2} = \frac{7+1}{2} =4[/latex], [latex] x_{1} =7-3=4[/latex], [latex] x_{2} =7-4=3[/latex].