SOLUTION: Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this. -x + 6y = 54 3x + y = 9 robert.russell19

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this. -x + 6y = 54 3x + y = 9 robert.russell19      Log On


   

Question 550785: Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this.
-x + 6y = 54
3x + y = 9
robert.russell1969@yahoo.com
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%283x%2By=9%2C-x%2B6y=54%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=9 Start with the first equation


y=9-3x Subtract 3x from both sides


y=-3x%2B9 Rearrange the equation



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

Since y=-3x%2B9, we can now replace each y in the second equation with -3x%2B9 to solve for x



-x%2B6highlight%28%28-3x%2B9%29%29=54 Plug in y=-3x%2B9 into the second equation. In other words, replace each y with -3x%2B9. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



-x%2B%286%29%28-3%29x%2B%286%29%289%29=54 Distribute 6 to -3x%2B9


-x-18x%2B54=54 Multiply


-19x%2B54=54 Combine like terms on the left side


-19x=54-54Subtract 54 from both sides


-19x=0 Combine like terms on the right side


x=%280%29%2F%28-19%29 Divide both sides by -19 to isolate x



x=0 Divide





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


So the first part of our answer is: x=0









Since we know that x=0 we can plug it into the equation y=-3x%2B9 (remember we previously solved for y in the first equation).



y=-3x%2B9 Start with the equation where y was previously isolated.


y=-3%280%29%2B9 Plug in x=0


y=0%2B9 Multiply


y=9 Combine like terms



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


So the second part of our answer is: y=9









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

So our answers are:

x=0 and y=9

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=9 (red) and -x%2B6y=54 (green) and the intersection of the lines (blue circle).