Question

решите систему уравнений
а) способами сложения x-5y=4 3x-8y=-2
б) способами подстановки 2x-5y=21 y=3x+1

Answer 1

$\displaystyle\bf\\1)\\\\\left \{ {{x-5y=4 \ |\cdot(-3)} \atop {3x-8y=-2}} \right.\\\\\\+\left \{ {{-3x+15y=-12} \atop {3x-8y=-2}} \right. \\-----------\\7y=-14\\\\y=-14:7=-2\\\\x=5y+4=5\cdot(-2)+4=-10+4=-6\\\\\\Otvet \ : \ (-6 \ ; \ -2)\\\\2)\\\\\left \{ {{2x-5y=21} \atop {y=3x+1}} \right. \\\\\\\left \{ {{2x-5\cdot(3x+1)=21} \atop {y=3x+1}} \right. \\\\\\\left \{ {{2x-15x-5=21} \atop {y=3x+1}} \right. \\\\\\\left \{ {{-13x=21+5} \atop {y=3x+1}} \right.$

$\displaystyle\bf\\\left \{ {{-13x=26} \atop {y=3x+1}} \right.\\\\\\\left \{ {{x=-2} \atop {y=3\cdot(-2)+1}} \right. \\\\\\\left \{ {{x=-2} \atop {y=-6+1}} \right. \\\\\\\left \{ {{x=-2} \atop {y=-5}} \right. \\\\\\Otvet \ : \ (-2 \ ; \ -5)$