a) 3x+2y=13 2x+y=11 |i -2 3x+2y=13 -4x-2y=-22 + _____________ x=9 2*9+y=11 x=9 y=11-18 x=9 y= - 7 b) 5x+3y=0 -x-2y=7 |*5 5x+3y=0 -5x-10y=35 + _________________ -7y=35 y= -5 -x-2*-5=7 y= -5 -x+10=7 y= -5 x= 3 y= -5 c) 3u+2v=2 |*-2 5u+4v=6 -6u-4v=-4 5u+4v=6 + ____________ -u=2 u= - 2 3*-2+2v=2 u= - 2 -6+2v=2 u= - 2 v=4 u= - 2 d) 3s+5t= -6 1.5s-2t=-3 |*-2 3s+5t= -6 -3s+4t= 6 + ____________ 9t=0 t=0 3s+5*0= -6 t=0 s= -2 t=0 e) 5=3x-y 5x-2y=7 3x-y=5 |*-2 5x-2y=7 -6x+2y= -10 5x-2y=7 + _______________ -x= -3 x=3 3*3-y=5 x=3 9-y=5 x=3 y= 4 x=3 f) x-3y=5 |*-3 y+3x= -5 -3x+9y= -15 3x+y= -5 + ________________ 10y= -20 y= -2 x-3*-2=5 y= -2 x+6=5 y= -2 x= -1 y= -2 Tylko nie zapomnij o klamerkach :) pls p. xD
a) 3x+2y=13 2x+y=11 / *(-2) 3x+2y=13 -4x -2y=-22 -------------- -x= -9 / *(-1) x=9 x=9 3 *9 +2y=13 x=9 2y= 13 -27 x=9 2y= -14 / :2 x=9 y= -7 b) 5x + 3y=0 -x -2y =7 / *5 5x+3y=0 -5x-10y=35 ------------ -7y=35/: (-7) y=-5 5x+3*(-5)=0 y=-5 5x=15/:5 y=-5 x=3 y=-5 c) 3u+2v=2 / *(-2) 5u+4v=6 -6u-4v=-4 5u+4v=6 ----------- -u=2 / *(-1) u=-2 u=-2 5*(-2)+4v=6 u=-2 4v=6+10 u=-2 4v= 16/:4 u=-2 v=4 d) 3s+5t=-6 1,5s-2t=-3 / * (-2) 3s+5t=-6 -3s+4t=6 ------------- 9t=0/:9 t=0 3s+5*0=-6 t=0 3s=-6/:3 t=0 s=-2 t=0 e) 5=3x-y 5x-2y=7 3x-y=5 / *(-2) 5x-2y=7 -6x+2y=-10 5x-2y=7 ----------- -x=-3 / * (-1) x=3 x=3 5*3-2y=7 x=3 -2y=7-15 x=3 -2y=-8 / (-2) x=3 y=4 f) x-3y=5 y+3x=-5 x-3y=5 3x+y=-5 /*3 x-3y=5 6x+3y=-15 ------------ 7x=10 /:7 x= 1 i 3/7 x=1 i 3/7 6* 1 i 3/7 +3y= -15 x= 1 i 3/7 3y= -15 -8 i 4/7 x= 1 i 3/7 3y= -23 i 4/7 /:3 x=1 i 3/7 y= 2 i 18/21
