SOLUTION: solve the system by the substitution method. Can you please show work! 2x+y=12 3x-y=13

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Question 316755: solve the system by the substitution method. Can you please show work!
2x+y=12
3x-y=13
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%282x%2By=12%2C3x-y=13%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

2x%2By=12 Start with the first equation


y=12-2x Subtract 2x from both sides


y=-2x%2B12 Rearrange the equation


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

Since y=-2x%2B12, we can now replace each y in the second equation with -2x%2B12 to solve for x



3x-highlight%28%28-2x%2B12%29%29=13 Plug in y=-2x%2B12 into the second equation. In other words, replace each y with -2x%2B12. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



3x%2B2x-12=13 Distribute the negative


5x-12=13 Combine like terms on the left side


5x=13%2B12Add 12 to both sides


5x=25 Combine like terms on the right side


x=%2825%29%2F%285%29 Divide both sides by 5 to isolate x



x=5 Divide





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


So the first part of our answer is: x=5









Since we know that x=5 we can plug it into the equation y=-2x%2B12 (remember we previously solved for y in the first equation).



y=-2x%2B12 Start with the equation where y was previously isolated.


y=-2%285%29%2B12 Plug in x=5


y=-10%2B12 Multiply


y=2 Combine like terms



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


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









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

So our answers are:

x=5 and y=2

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 2x%2By=12 (red) and 3x-y=13 (green) and the intersection of the lines (blue circle).