Răspuns:
4. a) [tex]\left \{ {{2x-3y+5=0} \atop {3x+y+13=0}} \right.[/tex] ⇒ y=-3x-13
2x-3(-3x-13)+5=0 2x+9x+39+5=0 11x=-44 /:11 x=-11
y=-3(-11)-13 y=33-13 y=20
9. a) [tex]\left \{ {{2(x-1)+3(y+\frac{1}{3})=4} \atop {12+6(y-\frac{1}{3})=4(x+1)}} \right.[/tex]
[tex]\left \{ {{2x-2+3\frac{3y+1}{3}=4} \atop {12+6\frac{3y-1}{3}=4x+4}} \right.[/tex]
[tex]\left \{ {{2x-2+3y+1=4} \atop {12+6y-2=4x+4}} \right.[/tex]
[tex]\left \{ {{2x+3y=5} \atop {-4x+6y=-6} /:(-2)} \right.[/tex]
[tex]\left \{ {{2x+3y=5} \atop {2x-3y=3}} \right.[/tex] ⇒ 2x=3y+3
3y+3+3y=5 6y=2/:2 ⇒ y= [tex]\frac{1}{3}[/tex]
2x= 3·[tex]\frac{1}{3}[/tex] +3 2x=1+3 2x=4/:2 x=2
b) [tex]\left \{ {{x-\frac{3}{4}(x-y+1)=y-2/*4} \atop {y-\frac{2}{3}(x-y-1)=x+3} /*3} \right.[/tex]
[tex]\left \{ {{4x-3x+3y-3=4y-8} \atop {3y-2y+2x+2=3x+9}} \right.[/tex]
[tex]\left \{ {{x-7y=-5} \atop {-x+y=7}} \right.[/tex] ⇒ x=y-7
y-7-7y=-5 6y=2/:2 ⇒ y= [tex]\frac{1}{3}[/tex]
x= [tex]\frac{1}{3}[/tex]-7 /·3 3x=-20 ⇒ x=[tex]-\frac{20}{3}[/tex]
Explicație pas cu pas:
