Răspuns:
d) [tex]\left \{ {{6(x-4)+2y = 3(y - 4)} \atop 4( x+2y) =5 (y+6)} \right.[/tex]
[tex]\left \{ {{6x-24+2y=3y-12} \atop {4x+2y=5y+30}} \right.[/tex]
[tex]\left \{ {{6x-y=12 /*(-3)} \atop {4x-3y=30}} \right.[/tex]
[tex]\left \{ {{-18x+3y=-36} \atop {4x-3y=30}} \right.[/tex]
-14x=-6 /:2 ⇒ [tex]x=\frac{3}{7}[/tex]
[tex]6*\frac{3}{7}-y=12 /*7[/tex]
18-7y=84
-7y=102 ⇒ [tex]y=-\frac{102}{7}[/tex]
e) [tex]\left \{ {{-3(x+y)-8=y+2} \atop {2(x+4)-2=-3y}} \right.[/tex]
[tex]\left \{ {{-3x-3y-8=y+2} \atop {2x+8-2=-3y}} \right.[/tex]
[tex]\left \{ {{-3x-4y=10 /*2} \atop {2x+3y=-6 /*3}} \right.[/tex]
[tex]\left \{ {{-6x-8y=20} \atop {6x+9y=-18}} \right.[/tex] ⇒ y=2
2x+3*2=-6
2x=-16 ⇒ x=-6
f) [tex]\left \{ {{5(x-4)+8=9y+10} \atop {4(y+2)+7=3x-1}} \right.[/tex]
[tex]\left \{ {{5x-20+8=9y+10} \atop {4y+8+7=3x-1}} \right.[/tex]
[tex]\left \{ {{5x-9y=22 /*3} \atop {-3x+4y=-16 /*5}} \right.[/tex]
[tex]\left \{ {{15x-27y=66} \atop {-15x+20y=-80}} \right.[/tex]
-7y=-14 /:(-7) ⇒ y=2
5x-9*2=22 5x-18=22 5x=40/:5 ⇒ x=8
Explicație pas cu pas:
