The equation $x + 2 y + 2 z = 1$ and $2 x + 4 y + 4 z = 9$ have

Only one solution

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One two solutions

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Infinite number of solutions

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None of these

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Solution

The correct option is D
None of these

Explanation for the correct option:
Find the number of solutions for the given system of equations.
Two equations are given:
$x + 2 y + 2 z = 1 . . . 1$
$2 x + 4 y + 4 z = 9 . . . 2$
From equation $1$ and equation $2$ .
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} = \frac{1}{2}$
but, $\frac{d_{1}}{d_{2}} = \frac{1}{9}$
So, $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} \neq \frac{d_{1}}{d_{2}}$
Therefore, the given system of equations has no solution.
Hence, the option $D$ is correct .

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