Question

Розв'яжіть систему рівнянь 3x² - 8y= -5, -2y + 5x = 3
срочноооо​

Answer 1

$\displaystyle\bf\\\left \{ {{3x^{2} -8y=-5} \atop {-2y+5x=3} \ |\cdot(-4)} \right. \\\\\\+\left \{ {{3x^{2} -8y=-5} \atop {-20x+8y=-12}} \right. \\------------\\3x^{2} -20x=-17\\\\3x^{2} -20x+17=0\\\\D=(-20)^{2} -4\cdot 3\cdot 17=400-204=196=14^{2}\\\\\\x_{1} =\frac{20-14}{6} =1\\\\\\x_{2}=\frac{20+14}{6} =5\frac{2}{3}\\\\\\2y=5x-3\\\\\\y=\frac{5}{2} x-\frac{3}{2} \\\\\\y_{1}=\frac{5}{2} \cdot 1-\frac{3}{2} =\frac{5}{2}-\frac{3}{2} =1$

$\displaystyle\bf\\y_{2}=\frac{5}{2}\cdot\frac{17}{3}-\frac{3}{2}=\frac{85}{6}-\frac{9}{6}=\frac{76}{6} =12\frac{2}{3} \\\\\\Otvet \ : \ \Big(1 \ ; \ 1\Big) \ \ , \ \ \Big(5\frac{2}{3} \ ; \ 12\frac{2}{3} \Big)$