Question

Розв'язати систему рівнянь

Answer 1

$\displaystyle\bf\\\left \{ {{\dfrac{2x-3}{2}+\dfrac{8+2y}{3} =5,5 } \atop {\dfrac{2y+2}{3}-\dfrac{5x+1}{4} =-2 }} \right. \\\\\\\left \{ {{\dfrac{2x-3}{2}\cdot 6+\dfrac{8+2y}{3}\cdot 6 =5,5 \cdot 6} \atop {\dfrac{2y+2}{3}\cdot 12-\dfrac{5x+1}{4} \cdot 12=-2\cdot 12 }} \right. \\\\\\\left \{ {{(2x-3)\cdot3+(8+2y)\cdot2=33} \atop {(2y+2)\cdot 4-(5x+1)\cdot 3=-24}} \right. \\\\\\\left \{ {{6x-9+16+4y=33} \atop {8y+8-15x-3=-24}} \right.$

$\displaystyle\bf\\\left \{ {{6x+4y=26} \ | \cdot(-2) \ \atop {-15x+8y=-29}} \right. \\\\\\+\left \{ {{-12x-8y=-52} \atop {-15x+8y=-29}} \right. \\-----------\\-27x=-81\\\\x=-81:(-27)=3\\\\4y=26-6x=26-6\cdot 3=26-18=8\\\\y=8:4=2\\\\Otvet: \ (3 \ ; \ 2)$