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Do the following pair of linear equation...

Do the following pair of linear equations have no solution ? Justify your answer.
(i) 2x + 4y = 3 and 12y +6x = 6
(ii) x = 2y and y = 2x
(iii) 3x + y - 3 = 0 and `2x + (2)/(3)y = 2`

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To determine whether the given pairs of linear equations have no solution, we will analyze each pair using the concept of ratios of coefficients. If the ratios of the coefficients of x, y, and the constant terms are equal, the equations represent the same line (infinite solutions). If the ratios of the coefficients of x and y are equal but the ratio of the constant terms is different, the equations are parallel and have no solution. Let's analyze each pair step by step. ### (i) Equations: 2x + 4y = 3 and 12y + 6x = 6 1. **Rearranging the second equation**: \[ 12y + 6x = 6 \implies 6x + 12y = 6 \implies 2x + 4y = 2 \] ...
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