1)
[tex]\left\{\begin{array}{l}x+y=1\\x^{2}+y^{2}+6y-7=0\\\end{array} \right.\\\\\left\{\begin{array}{l}x=1-y\\x^{2}+y^{2}+6y-7=0\\\end{array} \right.\\\\[/tex]
Podstawiamy wartość x:
[tex](1-y)^{2}+y^{2}+6y-7=0\\\\1-2y+y^{2}+y^{2}+6y-7=0\\\\-6+4y+2y^{2}=0~~~~|:(-2)\\\\3-2y-y^{2}=0\\\\-y^{2}-2y+3=0\\\\y^{2}+2y-3=0\\\\y^{2}+3y-y-3=0\\\\y(y+3)-(y+3)=0\\\\(y+3)(y-1)=0\\\\y+3=0~~~~~~~~~~~~y-1=0\\\\y=-3~~~~~~~~~~~~~~~~~~~y=1[/tex]
Podstawiamy y:
[tex]x=1-(-3)~~~~~~~~~~~~~~x=1-1\\\\x=4~~~~~~~~~~~~~~~~~~~~~~~~x=0[/tex]
ODP.:
[tex]x_{1}=\boxed{4}~~~~~~~~~~~~~~~~y_{1}=\boxed{-3}\\\\x_{2}=\boxed{0}~~~~~~~~~~~~~~~~y_{2}=\boxed{1}[/tex]
2)
[tex]\left\{\begin{array}{l}x-3y=-3\\x^{2}+y^{2}+8x-6y+15=0\\\end{array} \right.\\\\\left\{\begin{array}{l}x=-3+3y\\x^{2}+y^{2}+8x-6y+15=0\\\end{array} \right.[/tex]
Podstawiamy wartość x:
[tex](-3+3y)^{2}+y^{2}+8(-3+3y)-6y+15=0\\\\(3y-3)^{2}+y^{2}-24+24y-6y+15=0\\\\9y^{2}-18y+9+y^{2}-24+24y-6y+15=0\\\\10y^{2}=0\\\\y^{2}=0\\\\y=0[/tex]
Podstawiamy y:
[tex]x=-3+3*0\\\\x=-3[/tex]
ODP.:
[tex]x=\boxed{-3}~~~~~~~~~~~~~~~~y=\boxed{0}[/tex]
3)
[tex]\left\{\begin{array}{l}5x-2y=4\\x^{2}+y^{2}-10x+8y=-12\\\end{array} \right.\\\\\left\{\begin{array}{l}y=-2+\frac{5}{2}x\\x^{2}+y^{2}-10x+8y=-12\\\end{array} \right.[/tex]
Podstawiamy wartość y:
[tex]x^{2}+(-2+\frac{5}{2}x)^{2}-10x+8(-2+\frac{5}{2}x)=-12\\\\x^{2}+(\frac{5}{2}x-2)^{2}-10x-16+20x=-12\\\\x^{2}+\frac{25}{4}x^{2}-10x+4-10x-16+20x=-12\\\\\frac{29}{4}x^{2}-12=-12\\\\\frac{29}{4}x^{2}=0\\\\x^{2}=0\\\\x=0[/tex]
Podstawiamy x:
[tex]y=-2+\frac{5}{2}*0\\\\y=-2[/tex]
ODP.:
[tex]x=\boxed{0}~~~~~~~~~~~~~~~~y=\boxed{-2}[/tex]
