Question

Determine if the equations are intersecting, parallel, or coincident.

Answer 1

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.  
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