solve-the-simultaneous-equations-3x-y-9-x-2-xy-4-

Question Number 66755 by John Kaloki Musau last updated on 19/Aug/19

s o l v e t h e s i m u l t a n e o u s e q u a t i o n s :

3 x - y = 9

x^{2} - x y = 4

Answered by $@ty@m123 last updated on 20/Aug/19

x^{2} - x (3 x - 9) = 4

x^{2} - 3 x^{2} + 9 x = 4

2 x^{2} - 9 x + 4 = 0

x = \frac{9 \pm \sqrt{81 - 32}}{4} = \frac{9 \pm 7}{4} = 4, \frac{1}{2}

y = 3, - 7 \frac{1}{2}

Answered by John Kaloki Musau last updated on 21/Aug/19

y = 3 x - 9

x^{2} - 3 x^{2} + 9 x - 4 = 0

2 x^{2} - 8 x - x + 4 = 0

(2 x - 1) (x - 4) = 0

x = \frac{1}{2}, 4

x = 3 + \frac{1}{3} y

9 + 2 y + \frac{1}{9} y^{2} - 3 y - \frac{1}{3} y^{2} - 4 = 0

\frac{2}{9} y^{2} + y - 5 = 0

(y - 3) (2 y + 15) = 0

y = 3, - 7 \frac{1}{2}

Answered by Kunal12588 last updated on 20/Aug/19

| \begin{matrix} 3 & 1 \\ y & x \end{matrix} | = 9, | \begin{matrix} x & x \\ y & x \end{matrix} | = 4

\Rightarrow x | \begin{matrix} 1 & 1 \\ y & x \end{matrix} | = 4

\Rightarrow x | \begin{matrix} 3 & 1 \\ y & x \end{matrix} | - x | \begin{matrix} 2 & 0 \\ y & x \end{matrix} | = 4

\Rightarrow 9 x - 2 x^{2} = 4

\Rightarrow 2 x^{2} - 9 x + 4 = 0

\Rightarrow x = \frac{9 \pm \sqrt{81 - 32}}{4} = \frac{9 \pm 7}{4} = 4, \frac{1}{2}

p u t t i n g i n o n e o f t h e {e q}^{n}

y = 12 - 9 = 3 a n d y = \frac{3}{2} - 9 = - \frac{15}{2} = - 7 \frac{1}{2}

(\begin{matrix} x \\ y \end{matrix}) = (\begin{matrix} 4 & \frac{1}{2} \\ 3 & - 7 \frac{1}{2} \end{matrix})

Answered by Mr Jor last updated on 24/Aug/19

y = 3 x - 9

x^{2} - 3 x^{2} + 9 x = 4

2 x^{2} - 9 x + 4 = 0

(2 x - 1) (x - 4) = 0

x = \frac{1}{2}, 4

x = 3 + \frac{1}{3}

9 + 2 y + \frac{1}{9} y^{2} - 3 y - \frac{1}{3} y^{2} - 4 = 0

\frac{2}{9} y^{2} + y - 5 = 0

(y + 3) (2 y + 15) = 0

y = 3, - 7 \frac{1}{2}

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