[latex]egin{cases} x-4y =4 / *2 \ -2x+5y=-2 end{cases}\ \ egin{cases} 2x-8y =8 \ -2x+5y=-2 end{cases} \-------- \ -3y=6 /:(-3) \ \ y=-2[/latex] [latex]x-4*(-2) = 4 \ \x+8=4\ \x=4-8 \ \x= -4 \ \egin{cases} x = -4 \ y = -2 end{cases}[/latex] [latex]algebraicznie : \ \egin{cases} x-4y =-x+4 \ -2x+5y=-2 end{cases}\egin{cases} -4y =-x4 / : (-4) \ 5y=2x-2 /:5end{cases} \ \egin{cases} y =frac{1}{4}x -1 \ y= frac{2}{5} x-frac{2}{5} end{cases}[/latex] [latex]a)\ \ 4x^2 - 20x +25 =0\ \Delta = b^{2}-4ac = (-20)^{2}-4*4*25= 400-400=0 \ \x_{0}=frac{-b}{2a} =frac{20}{8}=frac{5}{2}=2frac{1}{2}[/latex] [latex]b)\ \ 2(2-x) < -x(x-3)\ \4-2x<-x^2+3x \ \ x^2-3x +4-2x<0\ \x^2-5x +4 <0 \ \Delta = b^{2}-4ac = (-5)^{2}-4*1*4=25-16=9[/latex] [latex]sqrt{Delta }=sqrt{9}=3\ \x_{1}=frac{-b-sqrt{Delta }}{2a} =frac{ 5-3}{2}=frac{2}{2}=1 \ \x_{2}=frac{-b-sqrt{Delta }}{2a} =frac{ 5+3}{2}=frac{8}{2}=4 \ \ a>0 ramiona paraboli skierowane do gory \ \xin (1,4)[/latex]
