Răspuns:
a) [tex]\left \{ {{\frac{x+2}{y+5}=\frac{x+1}{y} } \atop {2x-4y=7}} \right.[/tex]
[tex]\left \{ {{xy+2y=xy+5x+y+5} \atop {2x-4y=7}} \right.[/tex]
[tex]\left \{ {{-5x+y=5} \atop {2x-4y=7}} \right.[/tex] ⇒ y=5(x+1)
2x-20(x+1)=7
2x-20x-20=7
-18x=27 /:(-9) 2x=-3 ⇒ [tex]x=-\frac{3}{2}[/tex]
[tex]y=5(-\frac{3}{2} +1)=5(-\frac{1}{2})[/tex] ⇒ [tex]y=-\frac{5}{2}[/tex]
c) [tex]\left \{ {{2-3[4x+3(x-2y)]=11} \atop {\frac{5x+6}{2}-\frac{x-y}{3}=\frac{y}{6}} /*6} \right.[/tex]
[tex]\left \{ {{-3(4x+3x-6y)=9 /:(-3)} \atop {15x+18-2x+2y=y}} \right.[/tex]
[tex]\left \{ {{7x-6y=-3} \atop {13x+y=-18}} \right.[/tex]
y=-13x-18
7x-6(-13x-18)=-3
7x+78x+108=-3
85x=-111 ⇒ [tex]x=-\frac{111}{85}[/tex]
y=-13([tex]-\frac{111}{85}[/tex])-18 /*85
85y=1443-1530
85y=-87 ⇒ [tex]y=-\frac{87}{85}[/tex]
Explicație pas cu pas:
