Rozwiaz uklady rownan metoda podstawiania.; 1. {2x+y=10 {3x+3y=6 2. {4x-2y=10 {2x+2y=6

[latex]1)\\egin{cases} 2x+y=10 \ 3x+3y=6 end{cases}\\egin{cases} y=10-2x \ 3x+3y=6 end{cases}\\3x+3 (10-2x)=6 \3x+30-6x=6\-3x=6-30\-3x=-24 /:-3\x=8[/latex] [latex]egin{cases} x=8 \ y=10-2x end{cases}\\ egin{cases} x=8 \ y=10-2*8end{cases}\\ egin{cases} x=8 \ y=-6 end{cases}\\[/latex] [latex] 2)\\egin{cases} 4x-2y=10 \ 2x+2y=6 end{cases}\\ egin{cases}2y= 4x- 10 /:2 \ 2x+2y=6 end{cases}\\ egin{cases} y= 2x- 5 \ 2x+2y=6 end{cases}\\ 2x+2*(2x-5)=6\2x+4x-10=6\6x=6+10\6a=16 /:6\x=frac{16}{6}\x= =frac{8}{3}[/latex] [latex]egin{cases} x= frac{8}{3} \ y= 2x- 5 end{cases}\\ egin{cases} x= frac{8}{3} \ y= 2*frac{8}{3}- 5 end{cases}\\ egin{cases} x= frac{8}{3} \ y= frac{16}{3}- frac{15}{3} end{cases}\\ egin{cases} x= frac{8}{3} \ y= frac{1 }{3} end{cases}\\[/latex]

2x+y=10 3x+3y=6 y= 10 - 2x 3x + 3y= 6 y= 10 - 2x 3x + 3(10 - 2x) = 6 y= 10 - 2x 3x + 30 - 6x= 6 y= 10 - 2x 3x-6x = 6 - 30 y= 10 - 2x -3x= - 24 y= 10 - 2x x= - 24 : (-3) y= 10 - 2x x= 8 y= 10 - 2*8 x= 8 y= 10 - 16 x= 8 y= - 6 x= 8 spr 3x + 3y = 6 L = 3x + 3y = 3*8 + 3(-6) = 24 - 18 = 6 P = 6 6 = 6 L=P 4x - 2y = 10 2x + 2y = 6 4x - 2y = 10 2y = 6 - 2x 4x - (6 - 2x) = 10 2y = 6 - 2x 4x - 6+ 2x = 10 2y = 6- 2x 4x + 2x - 6= 10 2y = 6 - 2x 6x = 10 +6 2y = 6 - 2x 6x= 16 2y= 6 - 2x x= 16 : 6 2y= 6 - 2x x= 16/6 2y= 6 - 2x x= 2 i 4/6 2y= 6 – 2*16/6 x= 2 i 2/3 2y= 6 – 1 * 16/3 x= 2 i 2/3 2y = 6 – 16/3 x= 2 i 2/3 2y= 6 – 5 i 1/3 x= 2 i 2/3 2y= 2/3 x= 2 i 2/3 y= 2/3 : 2 x= 2 i 2/3 y = 2/3 * 1/2 x= 2 i 2/3 y = 2/6 x= 2 i 2/3 y= 1/3 spr. 2x + 2y = 6 L= 2x + 2y= 2 * 2 i 2/3 +2* 1/3 = 2*8/3 + 2/3= 16/3 + 2/3 = 18/3 = 6 P = 6 6 = 6 L=P