Răspuns:
a) [tex]\left \{ {{6x-y-6(x-9)=50} \atop {4(x+2y-1)-(x-3y+2)=164}} \right.[/tex]
[tex]\left \{ {{6x-y-6x+54=50} \atop {4x+8y-4-x+3y-2=164}} \right.[/tex]
[tex]\left \{ {{-y=-4} \atop {3x+11y=170}} \right.[/tex] ⇒ y=4
3x+11·4=170 3x=170-44 3x=126 /:3 ⇒ x=62
b) [tex]\left \{ {{3(x-2y+1)-5(x+y-2)=x+y-2} \atop {35x-49y=364 /:7}} \right.[/tex]
[tex]\left \{ {{3x-6y+3-5x-5y+10=x+y-2} \atop {5x-7y=52}} \right.[/tex]
[tex]\left \{ {{-3x-12y=-15 /:(-3)} \atop {5x-7y=52}} \right.[/tex]
[tex]\left \{ {{x+4y=5} \atop {5x-7y=52}} \right.[/tex] ⇒ x=5-4y
5(5-4y)-7y=52
25-20y-7y=52 -27y=27 ⇒ y=-1
x=5-4(-1) ⇒ x=1
c) [tex]\left \{ {{2(x-3y+1)=4x-y-205} \atop {\frac{3}{4}x-5*\frac{y+1}{6}=x-\frac{3}{5}y+\frac{1}{3} /*60}} \right.[/tex]
[tex]\left \{ {{2x-6y+2=4x-y-205} \atop {75x-50y-50=60x-36y+20}} \right.[/tex]
[tex]\left \{ {{-2x-5y=-203 /39} \atop {39x-14y=70 /*2}} \right.[/tex]
[tex]\left \{ {{-78x-192y=-7917} \atop {78x-28y=140}} \right.[/tex]
-220y=-7777 /:(-11) 20y=-707 ⇒ [tex]y=-\frac{707}{20}[/tex]
-2x-5([tex]-\frac{707}{20}[/tex])=-209 -2x-[tex]\frac{707}{4}[/tex]=-209 /*4
-8x-707=-836 /(-1)
8x=129 ⇒ [tex]x=\frac{129}{8}[/tex]
d) [tex]\left \{ {\frac{x+3}{y-1}=10} \atop {\frac{x-3}{y+1} =\frac{4}{3} }} \right.[/tex]
[tex]\left \{ {{x+3=10y-10} \atop {3x-9=4y+4}} \right.[/tex]
[tex]\left \{ {{x-10y=-13} \atop {3x-4y=13}} \right.[/tex] ⇒ x=10y-13
3(10y-13)-4y=13
30y-39-4y=13
26y=52 /:2 ⇒ y=2
x=10·2-13 ⇒ x=6
e) [tex]\left \{ {{(x+1)^{2}+y=x^{2} +1} \atop {3x+1=y+2}} \right.[/tex]
[tex]\left \{ {{x^{2}+2x+1+y=x^{2}+1} \atop {3x-y=1}} \right.[/tex]
[tex]\left \{ {{2x+y=0} \atop {3x-y=1}} \right.[/tex] ⇒ y=-2x
3x-(-2x)=1 5x=1 ⇒ [tex]x=\frac{1}{5}[/tex]
[tex]y=-2*\frac{1}{5}[/tex] ⇒ [tex]y=-\frac{2}{5}[/tex]
Explicație pas cu pas: