a) Intersecting linesSolution: For intersecting line, the linear equations should meet following condition:a2​a1​​=b2​b1​​For getting another equation to meet this criterion, multiply the coefficient of x with any number and multiply the coefficient of y with any other number. A possible equation can be as follows:4x+9y−8=0(b) Parallel linesSolution: For parallel lines, the linear equations should meet following condition:a2​a1​​= b2​b1​​=c2​c1​​For getting another equation to meet this criterion, multiply the coefficients of x and y with the same number and multiply the constant term with any other number. A possible equation can be as follows:4x+6y–24=0(c) Coincident linesSolution: For getting coincident lines, the equations should meet following condition;a2​a1​​= b2​b1​​=c2​c1​​For getting another equation to meet this criterion, multiply the whole equation with any number. A possible equation can be as follows:4x+6y–16=0