[tex]a) \ \left \{ {{x+3y=3} \atop {-x+2y=7}} \right.[/tex]
[tex]+ \left \{ {{x+3y=3} \atop {-x+2y=7}} \right.[/tex]
[tex]5y = 10 \ \ \ \ \ \ /:5[/tex]
[tex]y = 2[/tex]
[tex]x + 3y=3[/tex]
[tex]x +3*2=3[/tex]
[tex]x + 6 = 3[/tex]
[tex]x = 3-6[/tex]
[tex]x = -3[/tex]
[tex]Spr. \ -3 + 3*2= -3+6 = 3[/tex]
[tex]b) \ \left \{ {{2x-y=-4} \atop {x-2y=4 \ \ \ /*(-2) }} \right.[/tex]
[tex]+\left \{ {{2x-y=-4} \atop {-2x+4y=-8}} \right.[/tex]
[tex]3y = -12 \ \ \ \ \ \ /:3[/tex]
[tex]y = -4[/tex]
[tex]2x-y=-4[/tex]
[tex]2x-(-4)=-4[/tex]
[tex]2x+4=-4[/tex]
[tex]2x = -4-4[/tex]
[tex]2x = -8 \ \ \ \ \ \ \ /:2[/tex]
[tex]x=-4[/tex]
[tex]Spr. \ \ 2*(-4)-(-4) = -8+4=-4[/tex]
[tex]c) \left \{ {{5x-3y=-11 \ \ \ /*(-2)} \atop {2x+4y=6 \ \ \ /*5}} \right.[/tex]
[tex]+ \left \{ {{-10x+6y=22} \atop {10x+20y=30}} \right.[/tex]
[tex]26y = 52 \ \ \ \ \ \ \ /:26[/tex]
[tex]y=2[/tex]
[tex]2x+4y=6[/tex]
[tex]2x+4*2=6[/tex]
[tex]2x+8=6[/tex]
[tex]2x = 6 -8[/tex]
[tex]2x=-2 \ \ \ \ \ /:2[/tex]
[tex]x=-1[/tex]
[tex]Spr. \ \ 2*(-1)+4*2= -2+8 = 6[/tex]
[tex]d) \ \left \{ {{\frac{1}{4}x+3y=2,5 \ \ \ / *4 } \atop {\frac{1}{2}x-2y=3 \ \ \ /*(-2) }} \right.[/tex]
[tex]+\left \{ {{x+12y=10} \atop {-x+4y=-6}} \right.[/tex]
[tex]16y=4 \ \ \ \ \ \ \ /:16[/tex]
[tex]y = \frac{4}{16} = \frac{1}{4}[/tex]
[tex]\frac{1}{4}x+3*\frac{1}{4} =2,5[/tex]
[tex]\frac{1}{4}x +\frac{3}{4} = 2,5[/tex]
[tex]0,25x = 2,5-0,75[/tex]
[tex]0,25x = 1,75 \ \ \ \ \ \ /:0,25[/tex]
[tex]x = 7[/tex]
[tex]Spr. \ \ \frac{1}{2} *7 -2*\frac{1}{4} =\frac{7}{2} - \frac{2}{4} = \frac{7}{2} - \frac{1}{2} = \frac{6}{2} = 3[/tex]
Mam nadzieję, że pomogłam ;)
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