SOLUTION: Solve each system by the substitution method. x+3y=2 and -x+y=1

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve each system by the substitution method. x+3y=2 and -x+y=1      Log On


   

Question 175915: Solve each system by the substitution method.
x+3y=2 and -x+y=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 (note: I've rearranged the equations):

system%28-x%2By=1%2Cx%2B3y=2%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

-x%2By=1 Start with the first equation


y=1%2Bx Add x to both sides


y=%2Bx%2B1 Rearrange the equation


---------------------

Since y=x%2B1, we can now replace each y in the second equation with x%2B1 to solve for x



x%2B3highlight%28%28x%2B1%29%29=2 Plug in y=x%2B1 into the second equation. In other words, replace each y with x%2B1. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



x%2B%283%29%281%29x%2B%283%29%281%29=2 Distribute 3 to x%2B1


x%2B3x%2B3=2 Multiply


4x%2B3=2 Combine like terms on the left side


4x=2-3Subtract 3 from both sides


4x=-1 Combine like terms on the right side


x=%28-1%29%2F%284%29 Divide both sides by 4 to isolate x



x=-1%2F4 Reduce





-----------------First Answer------------------------------


So the first part of our answer is: x=-1%2F4









Since we know that x=-1%2F4 we can plug it into the equation y=x%2B1 (remember we previously solved for y in the first equation).



y=x%2B1 Start with the equation where y was previously isolated.


y=-1%2F4%2B1 Plug in x=-1%2F4


y=3%2F4 Combine like terms



-----------------Second Answer------------------------------


So the second part of our answer is: y=3%2F4









-----------------Summary------------------------------

So our answers are:

x=-1%2F4 and y=3%2F4

which form the ordered pair