SOLUTION: Please help I am getting confused...I need to solve each system by the substitution method. {{{x+3y=2}}} first {{{-x+y=1}}} second thanks so much

Algebra ->  Linear-equations -> SOLUTION: Please help I am getting confused...I need to solve each system by the substitution method. {{{x+3y=2}}} first {{{-x+y=1}}} second thanks so much      Log On


   

Question 124955: Please help I am getting confused...I need to solve each system by the substitution method.
x%2B3y=2 first
-x%2By=1 second
thanks so much
Found 2 solutions by iluvbuilding429, jim_thompson5910:
Answer by iluvbuilding429(41) About Me  (Show Source):
You can put this solution on YOUR website!
Please help I am getting confused...I need to solve each system by the substitution method.
x%2B3y=2 first
-x%2By=1 second
thanks so much


Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++1%5Cx+%2B+3%5Cy+=+2%2C%0D%0A++++-1%5Cx+%2B+1%5Cy+=+1+%29%0D%0A++We'll use substitution. After moving 3*y to the right, we get:
1%2Ax+=+2+-+3%2Ay, or x+=+2%2F1+-+3%2Ay%2F1. Substitute that
into another equation:
-1%2A%282%2F1+-+3%2Ay%2F1%29+%2B+1%5Cy+=+1 and simplify: So, we know that y=0.75. Since x+=+2%2F1+-+3%2Ay%2F1, x=-0.25.

Answer: system%28+x=-0.25%2C+y=0.75+%29.

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%28x%2B3y=2%2C-x%2By=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

x%2B3y=2 Start with the first equation


3y=2-x Subtract x from both sides


3y=-x%2B2 Rearrange the equation


y=%28-x%2B2%29%2F%283%29 Divide both sides by 3


y=%28%28-1%29%2F%283%29%29x%2B%282%29%2F%283%29 Break up the fraction


y=%28-1%2F3%29x%2B2%2F3 Reduce



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

Since y=%28-1%2F3%29x%2B2%2F3, we can now replace each y in the second equation with %28-1%2F3%29x%2B2%2F3 to solve for x



-x%2Bhighlight%28%28%28-1%2F3%29x%2B2%2F3%29%29=1 Plug in y=%28-1%2F3%29x%2B2%2F3 into the first equation. In other words, replace each y with %28-1%2F3%29x%2B2%2F3. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



%283%29%28-1x-%281%2F3%29x%2B2%2F3%29=%283%29%281%29 Multiply both sides by the LCM of 3. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



-3x-1x%2B2=3 Distribute and multiply the LCM to each side



-4x%2B2=3 Combine like terms on the left side


-4x=3-2Subtract 2 from both sides


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


x=%281%29%2F%28-4%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=%28-1%2F3%29x%2B2%2F3 (remember we previously solved for y in the first equation).



y=%28-1%2F3%29x%2B2%2F3 Start with the equation where y was previously isolated.


y=%28-1%2F3%29%28-1%2F4%29%2B2%2F3 Plug in x=-1%2F4


y=1%2F12%2B2%2F3 Multiply


y=3%2F4 Combine like terms and reduce. (note: if you need help with fractions, check out this solver)



-----------------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 point








Now let's graph the two equations (if you need help with graphing, check out this solver)


From the graph, we can see that the two equations intersect at . This visually verifies our answer.




graph of x%2B3y=2 (red) and -x%2By=1 (green) and the intersection of the lines (blue circle).