Question

Системные уравнения решите пж​

Answer 1

$\displaystyle\bf\\1)\\\\\left \{ {{4x-3y=-1} \atop {x-5y=4}} \right. \\\\\\\left \{ {{x=5y+4} \atop {4\cdot(5y+4)-3y=-1}} \right.\\\\\\\left \{ {{x=5y+4} \atop {20y+16-3y=-1}} \right. \\\\\\\left \{ {{x=5y+4} \atop {17y=-17}} \right. \\\\\\\left \{ {{x=5\cdot(-1)+4} \atop {y=-1}} \right.\\\\\\\left \{ {{x=-1} \atop {y=-1}} \right. \\\\\\Otvet: \ (-1 \ ; \ -1)$

$\displaystyle\bf\\2)\\\\\left \{ {{2x-5y=-7} \atop {x-3y=-5}} \right. \\\\\\\left \{ {{x=3y-5} \atop {2\cdot(3y-5)-5y=-7} \right.\\\\\\\left \{ {{x=3y-5} \atop {6y-10-5y=-7}} \right. \\\\\\\left \{ {{x=3y-5} \atop {y=3}} \right. \\\\\\\left \{ {{x=3\cdot 3-5} \atop {y=3}} \right.\\\\\\\left \{ {{x=4} \atop {y=3}} \right. \\\\\\Otvet: \ (4 \ ; \ 3)$

$\displaystyle\bf\\3)\\\\\left \{ {{3x-5y=16} \atop {2x+y=2|\cdot 5 \ }} \right. \\\\\\+\left \{ {{3x-5y=16} \atop {10x+5y=10}} \right. \\----------\\13x=26\\\\x=2\\\\y=2-2x=2-2\cdot 2=2-4=-2\\\\Otvet: \ (2 \ ; \ -2)\\\\\\4)\\\\\left \{ {{2x+5y=-7} \atop {3x-y=15} \ |\cdot 5} \right. \\\\\\+\left \{ {{2x+5y=-7} \atop {15x-5y=75}} \right. \\----------\\17x=68\\\\x=4\\\\y=3x-15=3\cdot 4-15=12-15=-3\\\\Otvet \ :(4 \ ; -3)$