Question

4x + 5y = 0 , 5x + 4y = 0 ...solve for the value of x and y

Answer 1

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Answer 2

$4x + 5y = 0 - - - - (i) \\ 5x + 4y = 0 - - - - (ii)$
From eq.(I)
$4x + 5y = 0 \\ 4x = - 5y \\ x = \frac{ - 5y}{4}$

put the value of x in eq.(ii)

$5x + 4y = 0 \\ 5 \times \frac{ - 5y}{4} + 4y = 0 \\ \frac{ - 25y}{4} + 4y = 0 \\ \frac{ - 25y + 16y}{4} = 0\\ \frac{ - 9y}{4} = 0 \\ - 9y = 0 \times 4 \\ y = \frac{0}{ - 9} \\ y = 0$

put the value of y in eq.(i)

$4x + 5y = 0 \\ 4x + 5 \times 0 = 0 \\ 4x = 0 \\ x = \frac{0}{4} \\ x = 0$