Solve the following pair of equations $31 x - 42 y = 51; 42 x - 31 y = 95$

x = 3, y = 1

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x = 2, y = 1

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x = 1, y = 1

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x = 6, y = 1

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Solution

The correct option is A $x = 3, y = 1$
$31 x - 42 y = 51$ ...(i)
$42 x - 31 y = 95$ ...(ii)
On adding (i) and (ii) , we get
$73 x - 73 y = 146$
$\Rightarrow x - y = 2$ ....(iii)
On subtracting (i) from (ii) , we get
$11 x + 11 y = 44$
$\Rightarrow x + y = 4$ ....(iv)
On adding (iii) and (iv) , we get
$2 x = 6$
$\Rightarrow x = 3$
By putting $x = 3$ in (iv), we get
$3 + y = 4$
$\Rightarrow y = 1$
$∴ x = 3, y = 1$

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Similar questions

Solve for the value of $x$ and $y$ : $31 x - 42 y = 51$ and $42 x - 31 y = 95$

Solve the following pair of equations:
$\frac{5}{x - 1} + \frac{1}{y - 2} = 2$
$\frac{6}{x - 1} - \frac{3}{y - 2} = 1$
(where $x \neq 1, y \neq 2)$

31 x + 47 y = 15 and 47 x + 31 y = 63,

\frac{5}{x - 1} + \frac{1}{y - 2} = 2

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\frac{4}{x} + 3 y = 8, \frac{6}{x} - 4 y = - 5

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