Решите систему уравнений. (x + 6y)^2 = 7y ( x + 6y )^2 = 7x

[latex] \left \{ {{(x+6y)^2=7y} \atop {(x+6y)^2=7x}} \right. \left \{ {{(x+6y)^2=7y} \atop {0=7x-7y}} \right. \left \{ {{(7x)^2=7x} \atop {x=y}} \right. \left \{ {{7x(7x-1)=0} \atop {x=y}} \right. [/latex] два случая: 1) [latex] \left \{ {{7x=0} \atop {x=y}} \right. \left \{ {{x=0} \atop {x=0}} \right. [/latex] 2) [latex] \left \{ {{7x-1=0} \atop {x=y}} \right. \left \{ {{x= \frac{1}{7} } \atop {y= \frac{1}{7} }} \right. [/latex] Ответ: [latex](0;0)[/latex] и [latex]( \frac{1}{7}; \frac{1}{7} )[/latex]