Question

Срочно.Решите систему уравнений:ху-у=24 х-3у = 7

Answer 1

Ответ:

$(13;2)$

$(-5;-4)$

Объяснение:

$\left \{ {{xy - y = 24} \atop {x - 3y=7}} \right. \left \{ {{xy - y = 24} \atop {x =7 + 3y}} \right. \Longrightarrow y(7 + 3y) - y = 24$

$y(7 + 3y) - y = 24$

$7y + 3y^{2} - y = 24$

$3y^{2} + 6y - 24 = 0|:3$

$y^{2} + 2y - 8 = 0$

$D = 4 - 4 * 1 * (-8) = 4 + 32 = 36 = 6^{2}$

$y_{1} = \frac{-2 + 6}{2} = \frac{4}{2} = 2$

$y_{2} = \frac{-2-6}{2} = \frac{-8}{2} = -4$

$x_{1} = 7 + 3y_{1} = 7 + 3 * 2 = 7 + 6 = 13$

$x_{2} = 7 + 3y_{2} = 7 + 3 * (-4) = 7 - 12 = -5$

$(13;2)$

$(-5;-4)$