1.
a)
[latex]egin{cases}(x-3)(x+3)+3y-x+2=(x-2)^2+y\ -2x+y=2end{cases}[/latex]
[latex]egin{cases}x^2-9+3y-x+2=x^2-4x+4+y\ -2x+y=2end{cases}[/latex]
[latex]egin{cases}x^2+3y-x-x^2+4x-y=4+9-2\ -2x+y=2end{cases}[/latex]
[latex]egin{cases}3x+2y=11\ y=2x+2end{cases}[/latex]
[latex]egin{cases}3x+2(2x+2)=11\ y=2x+2end{cases}[/latex]
[latex]egin{cases}3x+4x+4=11\ y=2x+2end{cases}[/latex]
[latex]egin{cases}3x+4x=11-4\ y=2x+2end{cases}[/latex]
[latex]egin{cases}7x=7 /:7\ y=2x+2end{cases}[/latex]
[latex]egin{cases}x=1\ y=2 cdot 1+2end{cases}[/latex]
[latex]egin{cases}x=1\ y=2+2end{cases}[/latex]
[latex]egin{cases}x=1\ y=4end{cases}[/latex]
============================
2.
a)
[latex] egin{cases}(x-4)(x+4)=(x+2)^2-y\ frac{2x-y}{2} - frac{x-y}{3}=1 / cdot 6end{cases} [/latex]
[latex] egin{cases}x^2-16=x^2+4x+4-y\3(2x-y)-2(x-y)=6end{cases}[/latex]
[latex] egin{cases}x^2-x^2-4x+y=4+16\6x-3y-2x+2y=6end{cases}[/latex]
[latex] egin{cases}-4x+y=20\4x-y=6end{cases}[/latex]
+_________
[latex]0=26[/latex]
Układ nie ma rozwiązania
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3.
a)
[latex]egin{cases}x+y=1\ x+3=-yend{cases}[/latex]
[latex]egin{cases}y=-x+1\ y=-x-3end{cases}[/latex]
ciąg dalszy w załączniku 1
b)
[latex]egin{cases}x-y=6\ frac{x-y}{3} - frac{x+y}{2} =5-x / cdot 6end{cases}[/latex]
[latex]egin{cases}y=x-6\ 2(x-y) -3(x+y) =6(5-x)end{cases}[/latex]
[latex]egin{cases}y=x-6\ 2x-2y -3x-3y =30-6xend{cases}[/latex]
[latex]egin{cases}y=x-6\ -2y -3y =30-6x-2x+3xend{cases}[/latex]
[latex]egin{cases}y=x-6\ -5y =-5x+30 /:(-5)end{cases}[/latex]
[latex]egin{cases}y=x-6\ y =x-6end{cases}[/latex]
ciąg dalszy w załączniku 2
c)
[latex]egin{cases}2(y-x)+4=2y\ y-(x+1)^2=2-(x-1)^2end{cases}[/latex]
[latex]egin{cases}2y-2x+4=2y\ y-x^2-2x-1=2-x^2+2x-1end{cases}[/latex]
[latex]egin{cases}2y-2y=2x-4\ y=2-x^2+2x-1+x^2+2x+1end{cases}[/latex]
[latex]egin{cases}0=2x-4\ y=4x+2end{cases}[/latex]
[latex]egin{cases}-2x=-4 /:(-2)\ y=4x+2end{cases}[/latex]
[latex]egin{cases}x=2\ y=4x+2end{cases}[/latex]
ciąg dalszy w załączniku 3
