Question

Rezolvati sistemele de ecuatii
1.
2x-y=2
4x+3y=6
2.
x-y=3
x+2y=6
3.
3x-5y=0
x-6y=-13



​

Answer 1

Răspuns:

Explicație pas cu pas:

1.

2x-y=2  ⇒2x-2=y   Inlocuim pe y in relatia de mai jos.  ⇒

4x+3y=6   ⇒4x+3(2x-2)=6  ⇒4x+6x-6=6  ⇒10x=12  ⇒x=12/10  ⇒y=2x-2=2·12/10-2= 24/10-20/10=4/10=2/5    x=12/10=6/5    y=4/10=2/5

Proba:       2x-y=2     2·6/5-2/5=12/5-2/5=10/5=2

2.

x-y=3  ⇒x=y+3   Inlocuim in relatia a doua

x+2y=6  ⇒y+3+2y=6  ⇒3y=6-3  ⇒3y=3  ⇒y=1  ⇒x=y+3=1+3=4

Proba: x+2y=6      4+2=6

3.

3x-5y=0

x-6y=-13  ⇒x=6y-13  Inlocuim pe x in 3x-5y=0  ⇒3(6y-13)-5y=0  ⇒18y-39-5y=0  ⇒13y=39  ⇒y=3  ⇒x=6·3-13=18-13=5   x=5  y=3

Proba: x-6y=-13    5-6·3=5-18=-13