Question

6.(2бали) Розв'яжіть систему рiвнянь

{x² + 2y = 5, y - x = 1​

Answer 1

Ответ:

$x {}^{2} + 2y = 5 \\ y - x = 1 \\ x {}^{2} + 2y = 5 \\ y = 1 + x \\ x {}^{2} + 2(1 + x) = 5 \\ x {}^{2} + 2 + 2x - 5 = 0 \\ x {}^{2} + 2x - 3 = 0 \\ x \times (x + 3) - (x + 3) = 0 \\ (x + 3)(x - 1) = 0 \\ x + 3 = 0 \\ x - 1 = 0 \\ x1 = - 3 \\ x2 = 1 \\ y1 = 1 + ( - 3) = - 2 \\ y2 = 1 + 1 = 2$

(-3;-2) (1;2)