Răspuns:
a) [tex]\left \{ {{3(x+2)+2y=y-5} \atop {2x+2(y-6)=3x-6}} \right.[/tex]
[tex]\left \{ {{3x+6+2y=y-5} \atop {2x+2y-12=3x-6}} \right.[/tex]
[tex]\left \{ {{3x+y=-11} \atop {-x+2y=6 /*3}} \right.[/tex]
[tex]\left \{ {{3x+y=-11} \atop {-3x+6y=18}} \right.[/tex]
7y=7 ⇒ y=1
3x+1=-11 3x=-12 ⇒ x=-4
b) [tex]\left \{ {{3x-2(x+y)=6} \atop {2(x-y) +4y=0}} \right.[/tex]
[tex]\left \{ {{3x-2x-2y=6} \atop {2x-2y +4y=0}} \right.[/tex]
[tex]\left \{ {{x-2y=6} \atop {2x+2y=0}} \right.[/tex]
3x=6 x=3
3-2y=6 2y=-3 y=[tex]-\frac{3}{2}[/tex]
c) [tex]\left \{ {{3(x+3)=2(y+5)} \atop {5(x+1)=4(y+1)}} \right.[/tex]
[tex]\left \{ {{3x+9=2y+10} \atop {5x+5=4y+4}} \right.[/tex]
[tex]\left \{ {{3x-2y=1/*(-2)} \atop {5x-4y=-1}} \right.[/tex]
[tex]\left \{ {{-6x+4y=-2} \atop {5x-4y=-1}} \right.[/tex]
-x=-3 x=3
3·3-2y=1 2y=8 y=4
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+8y=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]
22x=66 x=3
6·3-y=12 y=18-16 y=6
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=-12 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=-34 y=[tex]\frac{34}{7}[/tex]
5x-9· [tex]\frac{34}{7}[/tex]=22 /·7 35x-306=154 35x=460 x=[tex]\frac{92}{7}[/tex]
Explicație pas cu pas: