Find out the value of x and y $3 + x + x y = 0$ $3+x+xy=0$ $2 x + 5 y = 8$ $2x+5y=8$ ???

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Find out the value of x and y $3 + x + x y = 0$ $3+x+xy=0$ $2 x + 5 y = 8$ $2x+5y=8$ ???

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Answer 1 · 2017-10-12T13:26:40

$(- 1, 2), (\frac{15}{2}, - \frac{7}{5})$ $(-1,2),(15/2,-7/5)$

Explanation:

$3 + x + x y = 0 \to (1)$ $3+x+xy=0to(1)$

$2 x + 5 y = 8 \to (2)$ $2x+5y=8to(2)$

$rearrange equation (2) in terms of x or y$ $"rearrange equation "(2)" in terms of x or y"$

$\Rightarrow x = \frac{1}{2} (8 - 5 y) = 4 - \frac{5}{2} y \to (3)$ $rArrx=1/2(8-5y)=4-5/2yto(3)$

$substitute x = 4 - \frac{5}{2} y in (1)$ $"substitute "x=4-5/2y" in "(1)$

$\Rightarrow 3 + 4 - \frac{5}{2} y + 4 y - \frac{5}{2} y^{2} = 0$ $rArr3+4-5/2y+4y-5/2y^2=0$

$\Rightarrow - \frac{5}{2} y^{2} + \frac{3}{2} y + 7 = 0$ $rArr-5/2y^2+3/2y+7=0$

$multiply through by - 2$ $"multiply through by "-2$

$\Rightarrow 5 y^{2} - 3 y - 14 = 0$ $rArr5y^2-3y-14=0$

$\Rightarrow 5 y^{2} - 10 y + 7 y - 14 = 0 \leftarrow split middle term$ $rArr5y^2-10y+7y-14=0larr" split middle term"$

$factorise by grouping$ $"factorise by grouping"$

$5 y (y - 2) + 7 (y - 2) = 0$ $color(red)(5y)(y-2)color(red)(+7)(y-2)=0$

$factor out (y - 2)$ $"factor out "(y-2)$

$\Rightarrow (y - 2) (5 y + 7) = 0$ $rArr(y-2)(5y+7)=0$

$equate each factor to zero and solve for y$ $"equate each factor to zero and solve for y"$

$y - 2 = 0 \Rightarrow y = 2$ $y-2=0rArry=2$

$5 y + 7 = 0 \Rightarrow y = - \frac{7}{5}$ $5y+7=0rArry=-7/5$

$substitute these values into equation (3)$ $"substitute these values into equation "(3)$
$for corresponding values of x$ $"for corresponding values of x"$

$y = 2 \to x = 4 - 5 = - 1$ $y=2tox=4-5=-1$

$y = - \frac{7}{5} \to x = 4 + \frac{7}{2} = \frac{15}{2}$ $y=-7/5tox=4+7/2=15/2$

$\Rightarrow points of intersection (- 1, 2) and (\frac{15}{2}, - \frac{7}{5})$ $rArr"points of intersection "(-1,2)" and "(15/2,-7/5)$
graph{(3+x+xy)(y+2/5x-8/5)((x+1)^2+(y-2)^2-0.04)((x-15/2)^2+(y+7/5)^2-0.04)=0 [-10, 10, -5, 5]}

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Find out the value of x and y $3 + x + x y = 0$ $3+x+xy=0$ $2 x + 5 y = 8$ $2x+5y=8$ ???

Thanks in advance !

1 Answer

Explanation:

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Find out the value of x and y $3 + x + x y = 0$ $3+x+xy=0$ $2 x + 5 y = 8$ $2x+5y=8$ ???