Question

Rezolvati in multimea numerelor reale sistemul de ecuatii:
a){4x-y-24=2(5x-2y)
{3y-2=4-(x-y)

Answer 1

Ec. 1:
 4x - y - 24 = 2*(5x - 2y)
4x - y - 24 = 10x - 4y
4x - 10x - y + 4y = 24
-6x + 3y = 24 (se imparte ecuatia prin 3):
-2x + y = 8

Ec. 2:
3y - 2 = 4 - (x - y)
3y - 2 = 4 - x + y
x + 3y - y = 4 + 2
x + 2y = 6 (amplificam ecuatia cu 2):
2x + 4y = 12

Prin metoda reducerii, obtinem:
-2x + 2x + y + 4y = 8 + 12
5y = 20, de unde y = 20 / 5 = 4
x = 6 - 2y = 6 - 2*4 = 6 - 8 = -2
Raspuns: x = -2, y = 4