Find the values of a if the lines ax3y5 and 2x a1y6 are para

Solution

when  ax+3y=5 and 2x+ (a+1)y=6 are parallel

3y =-ax+5, (a+1)y =-2x +6

y =(-a/3)x+(5/3), y =(-2/(a+1))x +(6/(a+1))

when lines are parallel then their slope are equal

(-a/3) =(-2/(a+1))

a(a+1) =2*3

a²+a=6

a²+a -6=0

(a+3)(a-2)=0

a =-3, a =2

lines are parallel when a =-3, a =2

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when  ax+3y=5 and 2x+ (a+1)y=6 are parallel

3y =-ax+5, (a+1)y =-2x +6

y =(-a/3)x+(5/3), y =(-2/(a+1))x +(6/(a+1))

when lines are parallel then their product of slopes are equal to -1

(-a/3)(-2/(a+1)) =-1

2a/(3a+3)=-1

2a =-3a -3

5a =-3

a =-3/5

lines are perpendicular when a =-3/5