Question #b1629

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Question #b1629

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Answer 1 · 2017-03-16T20:39:52

$(- \frac{8}{3}, - \frac{5}{3}), (2, 3)$ $(-8/3, -5/3) , (2, 3)$

Explanation:

$y = x + 1$ $y=x+1$ => eq-1
$2 x^{2} + y^{2} = 17$ $2x^2+y^2=17$ => eq-2
Substitute $x + 1$ $x+1$ from 1 for $y$ $y$ in 2:
$2 x^{2} + {(x + 1)}^{2} = 17$ $2x^2+(x+1)^2=17$ => expand:
$2 x^{2} + x^{2} + 2 x + 1 = 17$ $2x^2+x^2+2x+1=17$ => simplify:
$3 x^{2} + 2 x - 16 = 0$ $3x^2+2x-16=0$ =>factor by grouping:
$3 x^{2} - 6 x + 8 x - 16 = 0$ $3x^2-6x+8x-16=0$
$3 x (x - 2) + 8 (x - 2) = 0$ $3x(x-2)+8(x-2)=0$
$(3 x + 8) (x - 2) = 0$ $(3x+8)(x-2)=0$
$x = - \frac{8}{3}, 2$ $x=-8/3, 2$ => substitute in 1 solve for $y$ $y$ :
$y = - \frac{5}{3}, 3$ $y=-5/3, 3$

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Question #b1629

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