Question

Дам 25 балов если поможете
Розв'язати систему рівнянь способом додавання: а) 4х - 5у = 2, 6х - 7у = -11; б) (m+1)/5 - (3n - 5)/10 = -2, (m-3)/6 + (5n - 9)/4 = 2.5

Answer 1

$\displaystyle\bf\\1)\\\\\left \{ {{4x-5y=2} \ |\cdot3\atop {6x-7y=-11} \ |\cdot(-2)} \right. \\\\\\+\left \{ {{12x-15y=6} \atop {-12x+14y=22}} \right. \\------------\\-y=28\\\\y=-28\\\\4x=2+5y=2+5\cdot(-28)=2-140=-138\\\\x=-138:4=-34,5\\\\Otvet: \ (-34,5 \ ; \ -28)$

$\displaystyle\bf\\2)\\\\\left \{ {{\dfrac{m+1}{5} -\dfrac{3n-5}{10} }=-2 \atop {\dfrac{m-3}{6} }+\dfrac{5n-9}{4}=2,5 } \right. \\\\\\\left \{ {{\dfrac{m+1}{5} \cdot 10-\dfrac{3n-5}{10} \cdot 10}=-2\cdot 10 \atop {\dfrac{m-3}{6} \cdot 12}+\dfrac{5n-9}{4}\cdot 12=2,5\cdot 12 } \right. \\\\\\\left \{ {{(m+1)\cdot 2-(3n-5)=-20} \atop {(m-3)\cdot 2+(5n-9)\cdot 3=30}} \right. \\\\\\\left \{ {{2m+2-3n+5=-20} \atop {2m-6+15n-27=30}} \right.$

$\displaystyle\bf\\\left \{ {{2m-3n=-27} \ |\cdot(-1)\atop {2m+15n=63}} \right. \\\\\\+\left \{ {{-2m+3n=27} \atop {2m+15n=63}} \right. \\----------\\18m=90\\\\m=5\\\\3n=2m+27=2\cdot 5+27=10+27=37\\\\n=12\frac{1}{3} \\\\Otvet: \ \Big(5 \ ; \ 12\frac{1}{3} \Big)$