The value of $y$ which will satisfy the equations
$2 x^{2} + 6 x + 5 y + 1 = 0$
$2 x + y + 3 = 0$
may be found by solving which one the following equations?

y^{2} + 14 y - 7 = 0

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y^{2} + 8 y + 1 = 0

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y^{2} + 10 y - 7 = 0

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y^{2} - 8 y + 7 = 0

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Solution

The correct option is C $y^{2} + 10 y - 7 = 0$
$2 x + y + 3 = 0 \Rightarrow x = \frac{- (y + 3)}{2} . . . (1)$
$2 x^{2} + 6 x + 5 y + 1 = 0$ Put 'x' from (1)
$\Rightarrow 2 [\frac{(y + 3)^{2}}{4}] + 3 (- y - 3) + 5 y + 1 = 0$
$\Rightarrow y^{2} + 6 y + 9 + 6 y - 18 + 10 y + 2 = 0$
$\Rightarrow y^{2} + 10 y - 7 = 0$

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The value of y which will satisfy the equations2x2+6x+5y+1=02x+y+3=0may be found by solving which one the following equations?

The correct option is C y2+10y−7=02x+y+3=0⇒x=−(y+3)2...(1)2x2+6x+5y+1=0 Put 'x' from (1)⇒2[(y+3)24]+3(−y−3)+5y+1=0⇒y2+6y+9+6y−18+10y+2=0⇒y2+10y−7=0

The value of $y$ which will satisfy the equations
$2 x^{2} + 6 x + 5 y + 1 = 0$
$2 x + y + 3 = 0$
may be found by solving which one the following equations?