Verified answer

[tex]\displaystyle\bf\\\left \{ {{x + 3y - 6= 2(x + y) - 9} \atop {0.5x - 2(y + 2) = 3(x - y) - 13 }} \right. \\ \displaystyle\bf\\\left \{ {{x + 3y = 2x + 2y - 9 + 6 \\} \atop { 0.5x - 2y - 4 = 3x - 3y - 13}} \right. \\ \displaystyle\bf\\\left \{ {{x - 2x + 3y - 2y = - 3} \atop {0.5x - 2y - 3x + 3y = - 13 + 4 }} \right. \\ \displaystyle\bf\\\left \{ {{ - x + y = - 3} \atop { - 2.5x + y = - 9 \: \: | \times (- 1)}} \right. \\ \displaystyle\bf\\ + \left \{ {{ - x + y = - 3} \atop {2.5x - y = 9 }} \right. \\ \\ 2.5x - x = 9 - 3 \\ 1.5x = 6 \\ x = 6 \div 1.5 \\ x = 4 \\ \\ - 4 + y = - 3 \\ y = - 3 + 4 \\ y = 1 \\ \displaystyle\bf\\otvet \: \left \{ {{x = 4} \atop {y= 1 }} \right. \\ \\ {x}^{2} + {y}^{2} = {4}^{2} + {1}^{2} = 16 + 1 = 17[/tex]