Solve the following equation.
$6^{x} + 6^{y} = 42, x + y = 3$ .

x=1,y=2

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x=1,y=1

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x=2,y= -1

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x=2,y=2

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Solution

The correct option is B x=1,y=2
Given $x + y = 3$

So, $6^{x} + 6^{y} = 42 \Rightarrow 6^{x} + 6^{3 - x} = 42$

Multiplying with $6^{x}$ , we get

$6^{2 x} - {42.6}^{x} + 216 = 0$

$\Rightarrow 6^{2 x} - {36.6}^{x} - {6.6}^{x} + 216 = 0$

$\Rightarrow 6^{x} (6^{x} - 6) - 6 (6^{x} - 6) = 0$

$\Rightarrow 6^{x} = 6 \Rightarrow x = 1$

Now, $x + y = 3 \Rightarrow y = 3 - x = 3 - 1 = 2$

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Solve the following equation.6x+6y=42,x+y=3.

The correct option is B x=1,y=2Given x+y=3So, 6x+6y=42⇒6x+63−x=42Multiplying with 6x, we get 62x−42.6x+216=0⇒62x−36.6x−6.6x+216=0⇒6x(6x−6)−6(6x−6)=0⇒6x=6⇒x=1Now, x+y=3⇒y=3−x=3−1=2

Solve the following equation.
$6^{x} + 6^{y} = 42, x + y = 3$ .