SOLUTION: Solve using the substitutiion method -3x+y=4 x+3y=22

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Question 395356: Solve using the substitutiion method
-3x+y=4
x+3y=22
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%28-3x%2By=4%2Cx%2B3y=22%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

-3x%2By=4 Start with the first equation


y=4%2B3x Add 3x to both sides


y=%2B3x%2B4 Rearrange the equation


y=%28%2B3x%2B4%29%2F%281%29 Divide both sides by 1


y=%28%28%2B3%29%2F%281%29%29x%2B%284%29%2F%281%29 Break up the fraction


y=3x%2B4 Reduce



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

Since y=3x%2B4, we can now replace each y in the second equation with 3x%2B4 to solve for x



x%2B3highlight%28%283x%2B4%29%29=22 Plug in y=3x%2B4 into the second equation. In other words, replace each y with 3x%2B4. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



x%2B%283%29%283%29x%2B%283%29%284%29=22 Distribute 3 to 3x%2B4


x%2B9x%2B12=22 Multiply


10x%2B12=22 Combine like terms on the left side


10x=22-12Subtract 12 from both sides


10x=10 Combine like terms on the right side


x=%2810%29%2F%2810%29 Divide both sides by 10 to isolate x



x=1 Divide





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


So the first part of our answer is: x=1









Since we know that x=1 we can plug it into the equation y=3x%2B4 (remember we previously solved for y in the first equation).



y=3x%2B4 Start with the equation where y was previously isolated.


y=3%281%29%2B4 Plug in x=1


y=3%2B4 Multiply


y=7 Combine like terms



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


So the second part of our answer is: y=7









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

So our answers are:

x=1 and y=7

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 -3x%2By=4 (red) and x%2B3y=22 (green) and the intersection of the lines (blue circle).



If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim