[(1)6x+7y=-4],[3x+8y=7]

Determine whether each pair of the following equations are solvable or not by finding the relations among the ratios of the co-efficients of the same variable and the constant terms of each pair. Also write whether the graphs of the equations of each pair are parallel or intersecting of coinciding or not: (i) 5x+3y=11, 2x-7y=-12, (ii) 6x-8y=2, 3x-4y=1, (iii) 8x-7y=0, 8x-7y=56,

Solve by cross-multiplication method. (i) 8x-3y=12,5x=2y +7 (ii) 6x+ 7y -11 =0, 5x+ 2y =13 (iii) (2)/(x)+(3)/(y) =5, (3)/(x) -(1)/(y) +9=0

Solve the following equations 5x-7y+z=11, 6x-8y-z=15, 3x+2y-6z=7 by Cramer's rule.

Classify the following pairs of lines as coincident, parallel, perpendicular or intersecting : (i) 6x+14y-16=0 , 12x+28y-32=0 (ii) 3x-4y=8 , 3x+4y=11 (iii) 5x-2y=7 , 2y-5x=-7 (iv) 4x+7y=19 , 7x-4y=-2 (v) x-2y=7 , 4y-2x=13

Find graphically the solution sets of each of the following systems of inequalities : x + y le 6 2x + 5y ge -8 3x + 8y le 9 10x + 12y le 7 8x + 7y le 14 x, y ge 10

Solve the following system of equations by matrix method : 5x+7y+2=0 4x+6y+3=0 5x+2y=3 3x+2y=5 3x+4y-5=0 x-y+3=0 3x+y=19 3x-y=23 3x+7y=4 x+2y=-1 3x+y=7 5x+3y=12

Solve the following pair of linear (simultaneous) equations using method of substitution : 6x = 7y + y 7y-x = 8

Consider the system of equations x-3y+z=-1 , 2x+y-4z=-1 , 6x-7y+8z=7

Solve the following system of equations using Cramers rule. 5x-7y+z=11 , 6x-8y-z=15 and 3x+2y-6z=7

Radius of the circle touching the lines 3x+4y-14=0,6x+8y+7=0 is