Răspuns :
Răspuns:
Metoda substitutiei:
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=-4
y=-3(-4)-13 y=12-13 ⇒y=-1
B) [tex]\left \{ {{2(x+y-1) -y=-3} \atop {3(x-y) -y=-3x}} \right.[/tex]
[tex]\left \{ {{2x+2y-2-y=-3} \atop {3x-3y-y=-3x}} \right.[/tex]
[tex]\left \{ {{2x+y=-1} \atop {6x-4y=0}} \right.[/tex] ⇒ y=-2x-1
6x-4(-2x-1)=0 6x+8x+4=0 14x=-4 /:2 ⇒ [tex]x=-\frac{7}{2}[/tex]
[tex]y=-2(-\frac{7}{2} )-1[/tex] y=7-1 ⇒ y=6
Metoda reducerii:
A) [tex]\left \{ {x+2y=11} \atop {8x-2y=-2}} \right.[/tex]
9x=9 ⇒ x=1
1+2y=11 2y=10 /:2 ⇒ y=5
B) [tex]\left \{ {{x+3y=-10} \atop {-x+2y=-5}} \right.[/tex]
5y=-15 /:5 ⇒ y=-3
x+3(-3)=-10 x=9-10 ⇒ x=-1
C) [tex]\left \{ {{2x-3y=7.5} \atop {5x+y=4.1 /*3}} \right.[/tex]
[tex]\left \{ {{2x-3y=7,5} \atop {15x+3y=12,3}} \right.[/tex]
17x=19,8 /*10 ⇒ [tex]x=\frac{198}{170}[/tex] ⇒ [tex]x=\frac{99}{85}[/tex]
[tex]5*\frac{99}{85} +y=4,1[/tex]
[tex]\frac{99}{17} +y=4,1 /*17[/tex]
99+17y=69,7 17y=-29,3/*10 ⇒ [tex]y=-\frac{293}{170}[/tex]
D) [tex]\left \{ {{2x+1=3y-7} \atop {3(x-y) +1=x+y-11}} \right.[/tex]
[tex]\left \{ {{2x-3y=-8} \atop {3x-3y-x-y=-12}} \right.[/tex]
[tex]\left \{ {{2x-3y=-8} \atop {4x-4y=-12 /:(-2)}} \right.[/tex]
[tex]\left \{ {{2x-3y=-8} \atop {-2x+2y=6}} \right.[/tex]
-y=-2 ⇒ y=2
2x-3*2=-8
2x=-2 ⇒ x=-1
E) [tex]\left \{ {{6x+7y=4} \atop {-2x+9y=-24 /*3}} \right.[/tex]
[tex]\left \{ {{6x+7y=4} \atop {-6x+27y=-72}} \right.[/tex]
34y=-68 /:34 ⇒ y=-2
6x+7(-2)=4 6x=4+14 6x=18/:3 ⇒ x=6
F) [tex]\left \{ {{3x-11y=-1 /*2} \atop {-2x+9y=17 /*3}} \right.[/tex]
[tex]\left \{ {{6x-22y=-2} \atop {-6x+27y=51}} \right.[/tex]
5y=49 ⇒ [tex]y=\frac{49}{5}[/tex]
[tex]3x-11*\frac{49}{5} =-1 /*5[/tex]
15x-539=-5
15x=534 /:3 5x=178 ⇒ [tex]x=\frac{178}{5}[/tex]
Explicație pas cu pas: