SOLUTION: Solve by substitution or elimination and specify which method you did: 6x + 2y = 10 5x - 3y = 27 (PS: Please show how you worked it out. I have been having mojor problems wit

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Question 142855: Solve by substitution or elimination and specify which method you did:
6x + 2y = 10
5x - 3y = 27
(PS: Please show how you worked it out. I have been having mojor problems with these kinds of questions. Thanks.)
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%286x%2B2y=10%2C5x-3y=27%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

6x%2B2y=10 Start with the first equation


2y=10-6x Subtract 6x from both sides


2y=-6x%2B10 Rearrange the equation


y=%28-6x%2B10%29%2F%282%29 Divide both sides by 2


y=%28%28-6%29%2F%282%29%29x%2B%2810%29%2F%282%29 Break up the fraction


y=-3x%2B5 Reduce



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

Since y=-3x%2B5, we can now replace each y in the second equation with -3x%2B5 to solve for x



5x-3highlight%28%28-3x%2B5%29%29=27 Plug in y=-3x%2B5 into the first equation. In other words, replace each y with -3x%2B5. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



5x%2B%28-3%29%28-3%29x%2B%28-3%29%285%29=27 Distribute -3 to -3x%2B5


5x%2B9x-15=27 Multiply


14x-15=27 Combine like terms on the left side


14x=27%2B15Add 15 to both sides


14x=42 Combine like terms on the right side


x=%2842%29%2F%2814%29 Divide both sides by 14 to isolate x



x=3 Divide





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


So the first part of our answer is: x=3









Since we know that x=3 we can plug it into the equation y=-3x%2B5 (remember we previously solved for y in the first equation).



y=-3x%2B5 Start with the equation where y was previously isolated.


y=-3%283%29%2B5 Plug in x=3


y=-9%2B5 Multiply


y=-4 Combine like terms



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


So the second part of our answer is: y=-4









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

So our answers are:

x=3 and y=-4

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 6x%2B2y=10 (red) and 5x-3y=27 (green) and the intersection of the lines (blue circle).