Question

Решите системы уравнений. Желательно на листочке в клеточку.задание Прикреплено.

Answer 1

$1) \left \{ {{4x-2y=2} \atop {2x+y=5}} \right. \\\\y=5-2x\\4x-2(5-2x)=2\\4x-10+4x=2\\8x=12\\x=1.5\\y=5-2*1.5\\y=2\\x+y=3.5$                              

$2) \left \{ {{3x-y=-1} \atop {-x+2y=7}} \right. \left \{ {{2(3x-y)=2(-1)} \atop {-x+2y=7}} \right. \left \{ {{6x-2y=-2} \atop {-x+2y=7}} \right. \\\\6x+(-x)=-2+7\\5x=5\\x=1\\-x+2y=7\\2y=7+x\\y=\frac{7+x}{2}\\y=\frac{7+1}{2} \\y=4\\x+y= 5$

$3)\left \{ {{3x+2y=8} \atop {4x-y=7}} \right. \left \{ {{3x+2y=8} \atop {2(4x-y)=2*7}} \right. \left \{ {{3x+2y=8} \atop {8x-2y=14}} \right. \\\\3x+8x=8+14\\11x=22\\x=2\\4x-y=7\\y=\frac{7-4x}{-1}=\frac{7-4*2}{-1}=\frac{7-8}{-1} =\frac{-1}{-1}=1\\y=1\\x+y=3$

$4) \left \{ {{5x-y=7} \atop {3x+2y=-1}} \right. \left \{ {{2(5x-y)=2*7} \atop {3x+2y=-1}} \right. \left \{ {{10x-2y=14} \atop {3x+2y=-1}} \right. \\\\10x+3x=14+(-1)\\13x=13\\x=1\\5x-y=7\\y=\frac{7-5x}{-1}=\frac{7-5*1}{-1} =\frac{2}{-1} =-2\\y=-2\\x+y=-1$

$5) \left \{ {{2x-y=1} \atop {3x+2y=12}} \right. \left \{ {{2(2x-y)=2*1} \atop {3x+2y=12}} \right. \left \{ {{4x-2y=2} \atop {3x+2y=12}} \right. \\\\4x+3x=2+12\\7x=14\\x=2\\2x-y=1\\y=\frac{1-2x}{-1}=\frac{1-2*2}{-1}=\frac{1-4}{-1}=\frac{-3}{-1}=3\\y=3\\x+y=5$

$6) \left \{ {{4x+y=10} \atop {x+3y=-3}} \right. \\y=10-4x\\x+3(10-4x)=-3\\x+30-12x=-3\\-11x=-33\\x=3\\y=10-4*3\\y=-2\\x+y=1$