Bună!
a) [tex]\left \{ {{4x-3y=13} \atop {2(x-y)+5y=-7}} \right. => \left \{ {{y=-\frac{13}{3}+\frac{4x}{3} } \atop {2(x-y)+5y=-7}} \right. => 2[x-(-\frac{13}{3}+\frac{4x}{3} )]+5(-\frac{13}{3} +\frac{4x}{3} )=-7[/tex]
[tex]<=> 2(^{3)} x+\frac{13}{3} -\frac{4x}{3} )-\frac{65}{3} +\frac{20x}{3} <=>[/tex]
[tex]<=> 2(-\frac{x}{3} +\frac{13}{3} )-\frac{65}{3} +\frac{20x}{3} =-7 <=>[/tex]
[tex]<=> -\frac{2x}{3} +\frac{26}{3} -\frac{65}{3} +\frac{20x}{3} =-7 <=>[/tex]
[tex]<=> 6x-13=-7/+13 => 6x=6 => x=1[/tex]
[tex]y=-\frac{13}{3} +\frac{4}{3} =-\frac{9}{3}=> y=-3[/tex]
b) [tex]\left \{ {{5(x+2)-3=y} \atop {x+2(y+1)=5}} \right. => \left \{ {{5x+10-3=y} \atop {x+2y+2=5}} \right. => \left \{ {{5x+7=y} \atop {x+2y=3}} \right. =>[/tex]
[tex]=> x+2(5x+7)=3 => x+10x+14=3 => 11x=-11 => x=-1[/tex]
[tex]y=5*(-1)+7=-5+7=> y=2[/tex]
→ substituție=înlocuire
