a) [latex]left { {{3x+2y=19} atop {5x-y=10}} ight[/latex] [latex]left { {{3x+2y=19} atop {-y=10-5x |*(-1)}} ight[/latex] [latex]left { {{3x+2y=19} atop {y=5x-10}} ight[/latex] [latex]left { {{3x+2(5x-10)=19} atop {y=5x-10}} ight[/latex] [latex]left { {{3x+10x-20=19} atop {y=5x-10}} ight[/latex] [latex]left { {{3x+10x=19+20} atop {y=5x-10}} ight[/latex] [latex]left { {{13x=39 |:13} atop {y=5x-10}} ight[/latex] [latex]left { {{x=3} atop {y=5*3-10}} ight[/latex] [latex]left { {{x=3} atop {y=15-10}} ight[/latex] [latex]left { {{x=3} atop {y=5}} ight[/latex] [latex]Spr.[/latex] [latex]left { {{3x+2y=19} atop {5x-y=10}} ight[/latex] [latex]3x+2y=19[/latex] [latex]L=3*3+2*5=9+10=19[/latex] [latex]P=19[/latex] [latex]L=P[/latex] [latex]5x-y=10[/latex] [latex]L=5*3-5=15-5=10[/latex] [latex]P=10[/latex] [latex]L=P[/latex] b) [latex]left { {{x-y-3=0} atop {2x+3y-11=0}} ight[/latex] [latex]left { {{x=y+3} atop {2(y+3)+3y-11=0}} ight[/latex] [latex]left { {{x=y+3} atop {2y+6+3y-11=0}} ight[/latex] [latex]left { {{x=y+3} atop {2y+3y=11-6}} ight[/latex] [latex]left { {{x=y+3} atop {5y=5 |:5}} ight[/latex] [latex]left { {{x=y+3} atop {y=1}} ight[/latex] [latex]left { {{x=1+3} atop {y=1}} ight[/latex] [latex]left { {{x=4} atop {y=1}} ight[/latex] [latex]Spr.[/latex] [latex]left { {{x-y-3=0} atop {2x+3y-11=0}} ight[/latex] [latex]x-y-3=0[/latex] [latex]L=4-1-3=0[/latex] [latex]P=0[/latex] [latex]L=P[/latex] [latex]2x+3y-11=0[/latex] [latex]L=2*4+3*1-11=8+3-11=0[/latex] [latex]P=0[/latex] [latex]L=P[/latex]
a) 3x + 2y = 19 5x - y = 10 y=5x-10 3x+2(5x-10)=19 y=5x-10 3x+10x-20=19 y=5x-10 13x=39 x=3 y=15-10=5 Spr.: 3*3+2*5=9+10=19 5*3-5=15-5=10 b) x - y - 3 = 0 2x + 3y -11 = 0 x=y+3 2(y+3)+3y-11=0 x=y+3 2y+6+3y-11=0 x=y+3 5y=5 y=1 x=4 Spr. 4-1-3=0 2*4+3*1-11=8+3-11=0
Rozwiąż układ równań metodą podstawiania i sprawdż poprawność rozwiązania: a) 3x + 2y = 19 5x - y = 10 5x -y = 10 3x+2y =19 -y = 10 -5x /*(-1) 3x+2y =19 y = 5x -10 3x +2(5x-10) =19 y = 5x -10 3x +10x -20 =19 y = 5x -10 13x = 19+20 y = 5x -10 x = 39 : 13 = 3 y = 5*3 -10 = 5 x = 3 x =3 y = 5 Spr. L1(3;5) = 3*3 +2*5 = 9 +10 =19 P1(3;5) =19 L1(3;5) = P1(3;5) L2(3;5) = 5*3 -5 = 15 -5 = 10 P2(3;5) = 10 L2(3;5) = P2(3;5) b) x - y - 3 = 0 2x + 3y -11 = 0 x = y +3 2*(y +3) +3y = 11 x = y +3 2y +6 +3y = 11 x = y +3 5y = 11-6 x = y +3 y = 5 :5 =1 x = 1 +3 = 4 y = 1 x = 4 y = 1 Spr L1(4;1) = 4 -1 -3 = 4 -4 = 0 P1(4;1) = 0 L1(4;1) = P1(4;1) L2(4;1) = 2*4 + 3*1 -11 = 8 +3 -11 = 11-11 = 0 P2(4;1) = 0 L2(4;1) = P2(4;1)
