Question

рашите 3 системы методом сложения
с обьяснением)​

Answer 1

Ответ:

• $\boldsymbol{(6;-1)}$
• $\boldsymbol{(8;1)}$
• $\boldsymbol{(1.2;0)}$

Объяснение:

$\boldsymbol{1.}$

  $\displaystyle \left \{ {{x-2y=8} \atop {3x+2y=16}} \right.$

   $(x-2y)+(3x+2y)=8+16\\x-2y+3x+2y=24\\(x+3x)+(2y-2y)=24\\4x=24| :4\\x=6$

   $x-2y=8\\6-2y=8\\-2y=8-6\\-2y=2| :(-2)\\y=-1$

$\boldsymbol{2.}$

   $\displaystyle \left \{ {{x-3y=5} \atop {4x+9y=41}} \right. \Leftrightarrow \left \{ {{x-3y=5| *3} \atop {4x+9y=41}} \right. \Leftrightarrow \left \{ {{3x-9y=15} \atop {4x+9y=41}} \right.$

   $(3x-9y)+(4x+9y)=15+41\\3x-9y+4x+9y=56\\(3x+4x)+(9y-9y)=56\\7x=56| :7\\x=8$

   $x-3y=5\\8-3y=5\\-3y=5-8\\-3y=-3| :(-3)\\y=1$

$\boldsymbol{3.}$

   $\displaystyle\left \{ {{10x+2y=12} \atop {-5x+4y=-6} \right. \Leftrightarrow \left \{ {{10x+2y=12} \atop {-5x+4y=-6|*2} \right. \Leftrightarrow\left \{ {{10x+2y=12} \atop {-10x+8y=-12}} \right.$

   $(10x+2y)+(-10x+8y)=12+(-12)\\10x+2y-10x+8y=12-12\\(10x-10x)+(2y+8y)=0\\10y=0| :10\\y=0$

   $10x+2y=12\\10x+2*0=12\\10x=12| :10\\x=1.2$