[tex]\left \{ {{x-3y=1-x-y} \atop {0,2x+0,1y=-0,1~~\vert \cdot 10}} \right. \\\\\left \{ {{x+x=1-y+3y} \atop {2x+y=-1}} \right. \\\\\left \{ {{2x=1+2y} \atop {y=-1-2x }} \right. \\\\\left \{ {{y=-1-2x } \atop {2x=1+2(-1-2x)}} \right. \\\\\left \{ {{y=-1-2x} \atop {2x=1-2-4x}} \right. \\\\\left \{ {{y=-1-2x} \atop {2x+4x=-1}} \right. \\\\\left \{ {{y=-1-2x} \atop {6x=-1~~\vert \div 6}} \right. \\\\\left \{ {{x=-\frac{1}{6} } \atop {y=-1-2x}} \right. \\\\[/tex]
[tex]\left \{ {{x=-\frac{1}{6} } \atop y=-1-2\cdot (- \frac{1}{6} )}} \right. \\\\\left \{ {{x=-\frac{1}{6} } \atop {y=-1+\frac{1}{3} }} \right. \\\\\left \{ {{x=-\frac{1}{6} } \atop {y=-\frac{2}{3} }} \right.[/tex]
Sprawdzam:
[tex]x= -\frac{1}{6} , ~~y=-\frac{2}{3} \\\\x-3y=1-x-y ~~\land~~x= -\frac{1}{6} ~~\land~~y=-\frac{2}{3}\\\\-\frac{1}{6}-3\cdot (-\frac{2}{3})=1-(-\frac{2}{3})-( -\frac{1}{6})\\\\ -\frac{1}{6}+2=1+\frac{2}{3}+\frac{1}{6}\\\\1\frac{5}{6} =1+\frac{4}{6} +\frac{1}{6}\\\\1\frac{5}{6} =1\frac{5}{6} \\\\L=P[/tex]
[tex]x= -\frac{1}{6} , ~~y=-\frac{2}{3} \\\\0,2x+0,1y=-0,1 ~~\land~~x= -\frac{1}{6} ~~\land~~y=-\frac{2}{3}\\\\\frac{2}{10} \cdot ( -\frac{1}{6}) + \frac{1}{10} \cdot (-\frac{2}{3})= -\frac{1}{10} ~~\mid \cdot 10\\\\-\frac{1}{3} -\frac{2}{3}=-1\\\\-1=-1\\\\L=P\\\\\\Odp: x= -\frac{1}{6} ~~\land~~y=-\frac{2}{3}[/tex]
