SOLUTION: Solve each of the following systems by substitution. 11. 4x – 12y = 5 -x + 3y = -1

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Question 123356: Solve each of the following systems by substitution.



11. 4x – 12y = 5
-x + 3y = -1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


Start with the given system of equations:

system%284x-12y=5%2C-x%2B3y=-1%29



Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.




So let's isolate y in the first equation

4x-12y=5 Start with the first equation


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


-12y=-4x%2B5 Rearrange the equation


y=%28-4x%2B5%29%2F%28-12%29 Divide both sides by -12


y=%28%28-4%29%2F%28-12%29%29x%2B%285%29%2F%28-12%29 Break up the fraction


y=%281%2F3%29x-5%2F12 Reduce



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Since y=%281%2F3%29x-5%2F12, we can now replace each y in the second equation with %281%2F3%29x-5%2F12 to solve for x



-x%2B3highlight%28%28%281%2F3%29x-5%2F12%29%29=-1 Plug in y=%281%2F3%29x-5%2F12 into the first equation. In other words, replace each y with %281%2F3%29x-5%2F12. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



-x%2B%283%29%281%2F3%29x%2B%283%29%28-5%2F12%29=-1 Distribute 3 to %281%2F3%29x-5%2F12


-x%2B%283%2F3%29x-15%2F12=-1 Multiply


%2812%29%28-1x%2B%283%2F3%29x-15%2F12%29=%2812%29%28-1%29 Multiply both sides by the LCM of 12. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



-12x%2B12x-15=-12 Distribute and multiply the LCM to each side



-15=-12 Combine like terms on the left side


0=-12%2B15Add 15 to both sides


0=3 Combine like terms on the right side


0=3 Simplify

Since this equation is never true for any x value, this means there are no solutions.