Question

21. Rezolvati prin metoda reducerii urmatoarele sisteme de ecuatii:

d) 6(x-4)+2y = 3(y - 4)
4( x+2y) =5 (y+6)
e) -3(x+y)-8=y+2
2(x+4)-2=-3y
f) 5(x-4)+8=9y+10
4(y+2)+7=3x-1.




​

Answer 1

Răspuns:

d) $\left \{ {{6(x-4)+2y = 3(y - 4)} \atop 4( x+2y) =5 (y+6)} \right.$

$\left \{ {{6x-24+2y=3y-12} \atop {4x+2y=5y+30}} \right.$

$\left \{ {{6x-y=12 /*(-3)} \atop {4x-3y=30}} \right.$

$\left \{ {{-18x+3y=-36} \atop {4x-3y=30}} \right.$

-14x=-6 /:2 ⇒ $x=\frac{3}{7}$

$6*\frac{3}{7}-y=12 /*7$

18-7y=84

-7y=102 ⇒ $y=-\frac{102}{7}$

e) $\left \{ {{-3(x+y)-8=y+2} \atop {2(x+4)-2=-3y}} \right.$

$\left \{ {{-3x-3y-8=y+2} \atop {2x+8-2=-3y}} \right.$

$\left \{ {{-3x-4y=10 /*2} \atop {2x+3y=-6 /*3}} \right.$

$\left \{ {{-6x-8y=20} \atop {6x+9y=-18}} \right.$ ⇒ y=2

2x+3*2=-6

2x=-16 ⇒ x=-6

f) $\left \{ {{5(x-4)+8=9y+10} \atop {4(y+2)+7=3x-1}} \right.$

$\left \{ {{5x-20+8=9y+10} \atop {4y+8+7=3x-1}} \right.$

$\left \{ {{5x-9y=22 /*3} \atop {-3x+4y=-16 /*5}} \right.$

$\left \{ {{15x-27y=66} \atop {-15x+20y=-80}} \right.$

-7y=-14 /:(-7) ⇒ y=2

5x-9*2=22   5x-18=22    5x=40/:5 ⇒ x=8

Explicație pas cu pas: