[tex]\left \{ {{2x + 3y=7(x-y)-35} \atop {x^2+y^2=10}} \right.[/tex]

[tex]\left \{ {{-5x + 10y=-35} \atop {x^2+y^2=10}} \right.[/tex]

[tex]\left \{ {{x = 7+2y} \atop {x^2+y^2=10}} \right.[/tex]

[tex](y+2y)^{2} +y^{2} = 10[/tex]

[tex]y_{1} = -3 \\y_2 = - \frac{13}{5}[/tex]

[tex]x_1 = 7+2*(-3)\\x_2 = 7 + 2 *(- \frac{13}{5})[/tex]

[tex]x_1 = 1\\x_2 = \frac{9}{5}[/tex]