Question 109909: I need some help PLEASE!!!!
solve each of the following by substitution
4x-12y=5
-x+3y=-1
Thanks
Heather Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website! 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
