Question 109909
4x-12y=5-------------------------eq1
-x+3y=-1 -------------------------eq2

O.K. now we will solve for x in eq2 and substitute the value for x into eq1:

-x+3y=-1  subtract 3y from both sides

-x+3y-3y=-1-3y  collect like terms

-x=-1-3y  multiply each term by -1

x=1+3y--------------------Now we will substitute this into eq1 and we get:

4(1+3y)-12y=5  get rid of parens (distributive law)
4+12y-12y=5--------------------WHOAA!!!!!!! SOMETHING IS WRONG.  THERE'S NO SOLUTION 

Lets put eq1 into slope-intercept form  (y=mx+b where m is the slope and b is the y-intercept, remember?)

4x-12y=5 subtract 4x from both sides

4x-4x-12y=5-4x  collect like terms

-12y=-4x+5  divide each term by -12
y=(4/12)x-5/12 or
y=(1/3)x-5/12   ----------------------eq1 in slope-intercept form
Slope of eq1 is 1/3

Now for eq2:

-x+3y=-1 add x to both sides
-x+x+3y=-1+x  collect like terms
3y=x-1  divide each term by 3
y=(1/3)x-1/3----------------------eq2 in slope-intercept

Slope of eq2 is 1/3

The two lines are parallel.  The equations are inconsistent---there is no solution


Hope this helps----ptaylor