Question

Розв'язати систему рівнянь.​

Answer 1

$\displaystyle\bf\\\left \{ {{\dfrac{x+3}{2}-\dfrac{y-2}{3} =2 } \atop {\dfrac{x-1}{4} +\dfrac{y+1}{3} =4}} \right. \\\\\\\left \{ {{\dfrac{x+3}{2}\cdot 6-\dfrac{y-2}{3}\cdot 6 =2\cdot 6 } \atop {\dfrac{x-1}{4}\cdot 12 +\dfrac{y+1}{3}\cdot 12 =4\cdot 12}} \right.\\\\\\\left \{ {{(x+3)\cdot 3-(y-2)\cdot2=12} \atop {(x-1)\cdot3+(y+1)\cdot 4=48}} \right. \\\\\\\left \{ {{3x+9-2y+4=12} \atop {3x-3+4y+4=48}} \right. \\\\\\\left \{ {{3x-2y=12-13} \atop {3x+4y=48-1}} \right.$

$\displaystyle\bf\\-\left \{ {{3x-2y=-1} \atop {3x+4y=47}} \right. \\----------\\3x-2y-3x-4y=-1-47\\\\-6y=-48\\\\y=-48:(-6)=8\\\\3x=2y-1=2\cdot 8-1=16-1=15\\\\x=15:3=5\\\\\\Otvet \ : \ (5 \ ; \ 8)$