Odpowiedź:
Zadanie 1.
a)
[tex]\left \{ {{x-y=2} \atop {2x+y=13}} \right. \\\left \{ {{x=2+y} \atop {2*(2+y)+y=13}} \right. \\\left \{ {{x=2+y} \atop {4+2y+y=13}} \right. \\\left \{ {{x=2+y} \atop {3y=9}} \right. \\\left \{ {{x=2+y} \atop {y=3 }} \right. \\\left \{ {{x=2+3 } \atop {y=3 }} \right. \\\\\left \{ {{x=5 } \atop {y=3 }} \right. \\[/tex]
b)
[tex]\left \{ {{3x-4y=15} \atop {7x+2y=1}} \right. \\\left \{ {{3x-4y=15} \atop {2y=1-7x}} \right. \\\left \{ {{3x-2*2y=15} \atop {2y=1-7x}} \right. \\\left \{ {{3x-2*(1-7x)=15} \atop {2y=1-7x}} \right. \\\left \{ {{3x-2+14x=15} \atop {2y=1-7x}} \right. \\\\\left \{ {{17x=17} \atop {2y=1-7x}} \right. \\\\\left \{ {{x=1} \atop {2y=1-7}} \right. \\\\\left \{ {{x=1} \atop {2y=-6}} \right. \\\\\left \{ {{x=1} \atop {y=-3}} \right.[/tex]
c)
[tex]\left \{ {{-2x+3y=5} \atop {6x-8y=3}} \right. \\\left \{ {{-2x=5-3y} \atop {6x-8y=3}} \right. \\\left \{ {{2x=-5+3y} \atop { {3*2x-8y=3}} \right. \\\left \{ {{2x=-5+3y} \atop { {3*(3y-5)-8y=3}} \right. \\\left \{ {{2x=-5+3y} \atop { {9y-15-8y=3}} \right. \\\left \{ {{2x=-5+3y} \atop { {y=18} \right. \\\left \{ {{2x=-5+3*18} \atop { {y=18} \right. \\\left \{ {{2x=-5+54} \atop { {y=18} \right. \\\left \{ {{2x=49} \atop { {y=18} \right. \\\left \{ {{x=\frac{49}{2} } \atop { {y=18} \right.[/tex]
Zadanie 2
[tex]\left \{ {{5x-2y=4} \atop {-x+0,4y=1}} \right. \\\left \{ {{5x-2y=4} \atop {x=-1+0,4y}} \right. \\\left \{ {{5*(0,4y-1)-2y=4} \atop {x=-1+0,4y}} \right. \\\left \{ {{2y-5-2y=4} \atop {x=-1+0,4y}} \right. \\\left \{ {{-5=4} \atop {x=-1+0,4y}} \right.[/tex]
SPRZECZNY
[tex]\left \{ {{1,5x-2y=6} \atop {x-\frac{4}{3}y=4 }} \right. \\\left \{ {{1,5x-2y=6} \atop {x=4+\frac{4}{3}y }} \right. \\\left \{ {{1,5*(4+\frac{4}{3}y)-2y=6} \atop {x=4+\frac{4}{3}y }} \right. \\\left \{ {{6+2y-2y=6} \atop {x=4+\frac{4}{3}y }} \right. \\\left \{ {{0=0} \atop {x=4+\frac{4}{3}y }} \right. \\\\[/tex]y∈R
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