Question

хелп!
/ - дробь
решите систему двух линейных уравнений с двумя переменными:
{ 3х-2у/5 + 5х-3у/3 = х+1
{2х-3у/3 + 4х-3у/2 = у+1

Answer 1

$\displaystyle\bf\\\left \{ {{\dfrac{3x-2y}{5} +\dfrac{5x-3y}{3} } =x+1\atop {\dfrac{2x-3y}{3}+\dfrac{4x-3y}{2} }=y+1} \right. \\\\\\\left \{ {{\dfrac{3x-2y}{5} \cdot 15+\dfrac{5x-3y}{3} } \cdot 15=(x+1)\cdot 15\atop {\dfrac{2x-3y}{3}\cdot 6+\dfrac{4x-3y}{2} \cdot 6 }=(y+1} )\cdot 6\right. \\\\\\\left \{ {{(3x-2y)\cdot 3+(5x-3y)\cdot5=15x+15} \atop {(2x-3y)\cdot 2+(4x-3y)\cdot 3=6y+6}} \right. \\\\\\\left \{ {{9x-6y+25x-15y=15x+15} \atop {4x-6y+12x-9y=6y+6}} \right.$

$\displaystyle\bf\\\left \{ {{19x-21y=15} \atop {16x-21y=6 \ |\cdot (-1)}} \right. \\\\\\+\left \{ {{19x-21y=15} \atop {-16x+21y=-6}} \right. \\------------\\3x=9\\\\x=9:3=3\\\\21y=16x-6=16\cdot 3-6=48-6=42\\\\y=42:21=2\\\\Otvet: \ (3 \ ; \ 2)$