SOLUTION: Solve using the substitution method. 3x-y=7 2x+5y =-1 solve in ordered pair as well. Thank you.

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Question 176203: Solve using the substitution method.

3x-y=7
2x+5y =-1 solve in ordered pair as well. Thank you.
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-y=7%2C2x%2B5y=-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

3x-y=7 Start with the first equation


-y=7-3x Subtract 3x from both sides


-y=-3x%2B7 Rearrange the equation


y=%28-3x%2B7%29%2F%28-1%29 Divide both sides by -1


y=%28%28-3%29%2F%28-1%29%29x%2B%287%29%2F%28-1%29 Break up the fraction


y=3x-7 Reduce



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

Since y=3x-7, we can now replace each y in the second equation with 3x-7 to solve for x



2x%2B5highlight%28%283x-7%29%29=-1 Plug in y=3x-7 into the second equation. In other words, replace each y with 3x-7. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



2x%2B%285%29%283%29x%2B%285%29%28-7%29=-1 Distribute 5 to 3x-7


2x%2B15x-35=-1 Multiply


17x-35=-1 Combine like terms on the left side


17x=-1%2B35Add 35 to both sides


17x=34 Combine like terms on the right side


x=%2834%29%2F%2817%29 Divide both sides by 17 to isolate x



x=2 Divide





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


So the first part of our answer is: x=2









Since we know that x=2 we can plug it into the equation y=3x-7 (remember we previously solved for y in the first equation).



y=3x-7 Start with the equation where y was previously isolated.


y=3%282%29-7 Plug in x=2


y=6-7 Multiply


y=-1 Combine like terms



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


So the second part of our answer is: y=-1









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

So our answers are:

x=2 and y=-1

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-y=7 (red) and 2x%2B5y=-1 (green) and the intersection of the lines (blue circle).