Răspuns:
a) [tex]\left \{ {{\frac{x}{2}=\frac{y}{3}} /*6 \atop {x+\frac{1}{4} =y+\frac{1}{7} } /*28} \right.[/tex]
[tex]\left \{ {{3x=2y} \atop {28x+7=28y+4}} \right.[/tex]
[tex]\left \{ {3x-2y=0 /*(-14)} \atop {28x-28y=-3}} \right.[/tex]
[tex]\left \{ {{-42x+28y=0} \atop {28x-28y=-3}} \right.[/tex]
-14x=-3 ⇒ [tex]x=\frac{14}{3}[/tex]
[tex]3*\frac{14}{3} =2y[/tex]
2y=14 ⇒ y=2
b) [tex]\left \{ {{\frac{x}{5}=\frac{y}{2}} /*10 \atop {\frac{x+1}{4}=\frac{y+1}{2}} /*4} \right.[/tex]
[tex]\left \{ {{2x=5y} \atop {x+1=2y+2}} \right.[/tex]
[tex]\left \{ {{2x-5y=0} \atop {x-2y=1}} \right.[/tex] ⇒ x=2y+1
2(2y+1)-5y=0 4y+2-5y=0 ⇒ y=2, x=5
c) [tex]\left \{ {{\frac{x-2}{3}=\frac{y}{2} /*6} \atop {\frac{x}{2}=\frac{y-2}{8} } /*8} \right.[/tex]
[tex]\left \{ {{2x-4=3y} \atop {4x=y-2}} \right.[/tex] ⇒ y=4x+2
2x-3(4x+2)=4 2x-12x-6=4 -10x=10 ⇒ x=-1, y=-2
d) [tex]\left \{ {{\frac{4-x}{5}=\frac{y+12}{10} /*10} \atop {\frac{y+1}{3}=\frac{-x}{6}/*6 }} \right.[/tex]
[tex]\left \{ {{8-2x=y+12} \atop {2y+2=-x}} \right.[/tex] ⇒ x=-2(y+1)
8-2(-2)(y+1)=y+12 8+4y+4=y+12 3y=0 ⇒ y=0; x=-2
e) [tex]\left \{ {{\frac{x}{2}+1=\frac{y+2}{2} /*2} \atop {2x+3y=\frac{5}{2}/* 2}} \right.[/tex]
[tex]\left \{ {{x+2=y+2} \atop {4x+6y=5}} \right.[/tex] ⇒ x=y
4x+6x=5 10x=5 /:5 2x=1 ⇒ [tex]x=y=\frac{1}{2}[/tex]
f) [tex]\left \{ {{\frac{2x}{3}+y =\frac{y}{3} /*3 } \atop {4x+6y=1}} \right.[/tex]
[tex]\left \{ {{2x+3y=y} \atop {4x+6y=1}} \right.[/tex]
[tex]\left \{ {{2x=-2y} /:2 \atop {4x+6y=1}} \right.[/tex] ⇒ x=-y
4x-6x=1 2x=-1 ⇒ [tex]x=-\frac{1}{2}[/tex], [tex]y=\frac{1}{2}[/tex]
Explicație pas cu pas:
