Question

Am nevoie urgent!!! Dau puncte maxim si coroana, cu rezolvare

Answer 1

$1)~\left\{\begin{array}{ccc}4x+3y=2|\cdot(-7)\\5x+7y=9|\cdot3\\\end{array}\right.\Rightarrow \left\{\begin{array}{ccc}-28x-21y=-14\\15x+21y=27\\\end{array}\right. \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~----------\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-13x ~~~/~~=13\Rightarrow x=-\dfrac{13}{13} \Rightarrow \boxed{x=-1}\\\\x=-1\Rightarrow 4x+3y=2\Rightarrow 4\cdot(-1)+3y=2\Rightarrow -4+3y=2\Rightarrow \\\\\Rightarrow 3y=2+4 \Rightarrow 3y=6\Rightarrow y=\dfrac{6}{3} \Rightarrow \boxed{y=2}$

$2)~\left\{\begin{array}{ccc}6x-3y=6\\-2x+y=-2|\cdot 3\\\end{array}\right.\Rightarrow \left\{\begin{array}{ccc}6x-3y=6\\-6x+y=-2\\\end{array}\right.\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~--------\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~/~-2y=4\Rightarrow y=-\dfrac{4}{2} \Rightarrow \boxed{y=-2}\\\\y=-2\Rightarrow 6x-3y=6\Rightarrow 6x-3\cdot(-2)=6\Rightarrow 6x+6=6\Rightarrow \\\\\Rightarrow 6x=6-6\Rightarrow 6x=0\Rightarrow x=\dfrac{0}{6}\Rightarrow \boxed{x=0}$

$3)~\left\{\begin{array}{ccc}x+2y=-6\\3x-y=38|\cdot2\\\end{array}\right.\Rightarrow \left\{\begin{array}{ccc}x+2y=-6\\6x-2y=76\\\end{array}\right.\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~--------\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~7x~~~~/~=70\Rightarrow x=\dfrac{70}{7} \Rightarrow \boxed{x=10}\\\\x=10\Rightarrow x+2y=-6\Rightarrow 10+2y=-6\Rightarrow 2y=-6-10\Rightarrow\\\\\Rightarrow 2y=-16\Rightarrow y=-\dfrac{16}{2}\Rightarrow \boxed{y=-8}$

$4)~\left\{\begin{array}{ccc}-x+10y=7|\cdot3\\3x-4y=5\\\end{array}\right.\Rightarrow \left\{\begin{array}{ccc}-3x+30y=21\\3x-4y=5\\\end{array}\right.\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~---------\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~/~~~~~26y=26\Rightarrow y=\dfrac{26}{26}\Rightarrow \boxed{y=1} \\\\y=1\Rightarrow 3x-4y=5\Rightarrow 3x-4\cdot1=5\Rightarrow 3x-4=5\Rightarrow 3x=5+4\Rightarrow \\\\\Rightarrow 3x=9\Rightarrow x=\dfrac{9}{3} \Rightarrow \boxed{x=3}$

$5)~\left\{\begin{array}{ccc}-4x+5y=17|\cdot3\\-3x+2y=4|\cdot(-4)\\\end{array}\right.\Rightarrow \left\{\begin{array}{ccc}-12x+15y=51\\12x-8y=-16\\\end{array}\right.\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~----------\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~/~~~~~~7y=35\Rightarrow y=\dfrac{35}{7}\Rightarrow \boxed{y= 5}\\\\y=5\Rightarrow -3x+2y=4\Rightarrow -3x+2\cdot5=4\Rightarrow -3x+10=4\Rightarrow \\\\\Rightarrow -3x=4-10\Rightarrow -3x=-6\Rightarrow x=\dfrac{6}{3} \Rightarrow \boxed{x=2}$

$6)~\left\{\begin{array}{ccc}7x+2y=-4|\cdot5\\3x-5y=10|\cdot2\\\end{array}\right.\Rightarrow \left\{\begin{array}{ccc}35x+10y=-20\\6x-10y=20\\\end{array}\right.\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~---------\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~41x~~~~/~~~=0\Rightarrow x=\dfrac{0}{41} \Rightarrow \boxed{x=0}\\\\x=0\Rightarrow 3x-5y=10\Rightarrow 3\cdot0-5y=10\Rightarrow 0-5y=10\Rightarrow -5y=10-0\Rightarrow\\\\\Rightarrow -5y=10\Rightarrow y=-\dfrac{10}{5} \Rightarrow \boxed{y=-2}$