[tex]\displaystyle\bf\\\left \{ {{(x - 4)y + 13 = x(y - 3) + 15 - 2(x - 4)} \atop {x + 5 + xy = 8x - 9 + y(x + 5) }} \right. \\ \displaystyle\bf\\\left \{ {{xy - 4y + 13 = xy - 3x + 15 - 2x + 8} \atop {x + 5 + xy = 8x - 9 + xy + 5y }} \right. \\ \displaystyle\bf\\\left \{ {{xy - 4y - xy + 3x + 2x = 23 - 13} \atop {x + xy - 8x - xy - 5y = - 9 - 5 }} \right. \\ \displaystyle\bf\\\left \{ {{5x - 4y = 10} \atop { - 7x - 5y = - 14 }} \right. \\ \\ [/tex]

1) Метод подстановки:

[tex]\displaystyle\bf\\\left \{ {{x = 2 + 0.8y} \atop { - 7(2 + 0.8y)- 5y = - 14 }} \right. \\ \\ - 14 - 5.6y - 5y = - 14 \\ - 10.6y = - 14 + 14 \\ - 10.6y = 0 \\ y = 0 \\ \\ x = 2 + 0.8 \times 0 \\ x = 0[/tex]

2) Метод сложения:

[tex]\displaystyle\bf\\\left \{ {{5x - 4y = 10 \: \: | \times 7 } \atop { - 7x - 5y = - 14 \: \: | \times 5 }} \right. \\ \displaystyle\bf\\ + \left \{ {{35x - 28y = 70} \atop { - 35x - 25y = - 70 }} \right. \\ \\ - 28y - 25y = 70 - 70 \\ - 53y = 0 \\ y = 0 \\ \\ 5x - 4 \times 0 = 10 \\ 5x = 10 \\ x = 10 \div 5 \\ x = 2[/tex]

Ответ: ( 2 ; 0 )