Obtain real solutions of simultaneous equations.
$x y + 3 y^{2} - x + 4 y - 7 = 0$
$2 x y + y^{2} - 2 x - 2 y + 1 = 0$ .

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Solution

Multiplying $(1)$ by $2$ and subtracting from $(2)$ ,
we get $5 y^{2} + 10 y - 15 = 0$
or $y^{2} + 2 y - 3 = 0$
or $(y + 3) (y - 1) = 0$
$∴ y = - 3$
and hence $x = 2$ . Note $y \neq 1$ as $y = 1$ will make x infinite or reduce the equation to an identify.

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Obtain real solutions of simultaneous equations.xy+3y2−x+4y−7=02xy+y2−2x−2y+1=0.

Multiplying (1) by 2 and subtracting from (2), we get 5y2+10y−15=0or y2+2y−3=0or (y+3)(y−1)=0∴y=−3and hence x=2. Note y≠1 as y=1 will make x infinite or reduce the equation to an identify.

Obtain real solutions of simultaneous equations.
$x y + 3 y^{2} - x + 4 y - 7 = 0$
$2 x y + y^{2} - 2 x - 2 y + 1 = 0$ .

Multiplying $(1)$ by $2$ and subtracting from $(2)$ ,
we get $5 y^{2} + 10 y - 15 = 0$
or $y^{2} + 2 y - 3 = 0$
or $(y + 3) (y - 1) = 0$
$∴ y = - 3$
and hence $x = 2$ . Note $y \neq 1$ as $y = 1$ will make x infinite or reduce the equation to an identify.