Since bx does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting bx from both sides. 
-ay=-bx+2 
ax+by=3 
Divide each term in the equation by -1a. 
y=(bx-2)/(a) 
ax+by=3 
Divide each term in the numerator by the denominator. 
y=(bx)/(a)-(2)/(a) 
ax+by=3 
The equation is not linear, so the slope does not exist. 
No slope can be found. 
ax+by=3 
Since ax does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting ax from both sides. 
No slope can be found. 
by=-ax+3 
Remove the common factors that were cancelled out. 
No slope can be found. 
y=-(ax)/(b)+(3)/(b) 
Divide each term in the equation by b. 
No slope can be found. 
y=(-ax+3)/(b) 
Divide each term in the numerator by the denominator. 
No slope can be found. 
y=-(ax)/(b)+(3)/(b) 
The equation is not linear, so the slope does not exist. 
No slope can be found. 
No slope can be found. 
Compare the slopes (m) of the two equations. 
m1=, m2= 
The equations are parallel because the slopes of the two lines are equal. 
FROM YAHOO ANSWER