On comparing the ratios \(\dfrac{a_1}{a_2}\), \(\dfrac{b_1}{b_2}\), and \(\dfrac{c_1}{c_2}\), find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:
(i) \(5x – 4y + 8 = 0\) , \(7x + 6y – 9 = 0\) (ii) \(9x + 3y + 12 = 0\), \(18x + 6y + 24 = 0\) (iii) \(6x – 3y + 10 = 0\), \(2x – y + 9 = 0\)
On comparing the ratios\( \dfrac{a_1}{a_2},\) \(\dfrac{b_1}{b_2}\), and \(\dfrac{c_1}{c_2}\), find out whether the following pair of linear equations are consistent, or inconsistent.(i) \(3x + 2y = 5 ; 2x – 3y = 7\) (ii) \(2x – 3y = 8 ; 4x – 6y = 9\) (iii) \(\dfrac{3}{2x} + \dfrac{5}{3y} =7\) ; \(9x – 10y = 14\) (iv) \(5x – 3y = 11 \) ;\( – 10x + 6y = –22\) (v)\( \dfrac{4}{3x} +2y =8; 2x + 3y = 12\)
Half the perimeter of a rectangular garden, whose length is \(4 \) m more than its width is \(36\) m. Find the dimensions of the garden