SOLUTION: Solve the equations for x and y or state that there is no solution. 3x + 7y = 5 2x - y = 1

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Question 183044: Solve the equations for x and y or state that
there is no solution.
3x + 7y = 5
2x - y = 1
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%2B7y=5%2C2x-y=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 second equation

2x-y=1 Start with the second equation


-y=1-2x Subtract 2x from both sides


-y=-2x%2B1 Rearrange the equation


y=%28-2x%2B1%29%2F%28-1%29 Divide both sides by -1


y=%28%28-2%29%2F%28-1%29%29x%2B%281%29%2F%28-1%29 Break up the fraction


y=2x-1 Reduce



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

Since y=2x-1, we can now replace each y in the first equation with 2x-1 to solve for x



3x%2B7highlight%28%282x-1%29%29=5 Plug in y=2x-1 into the first equation. In other words, replace each y with 2x-1. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



3x%2B%287%29%282%29x%2B%287%29%28-1%29=5 Distribute 7 to 2x-1


3x%2B14x-7=5 Multiply


17x-7=5 Combine like terms on the left side


17x=5%2B7Add 7 to both sides


17x=12 Combine like terms on the right side


x=%2812%29%2F%2817%29 Divide both sides by 17 to isolate x




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


So the first part of our answer is: x=12%2F17









Since we know that x=12%2F17 we can plug it into the equation y=2x-1 (remember we previously solved for y in the first equation).



y=2x-1 Start with the equation where y was previously isolated.


y=2%2812%2F17%29-1 Plug in x=12%2F17


y=24%2F17-1 Multiply


y=7%2F17 Combine like terms (note: if you need help with fractions, check out this solver)



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


So the second part of our answer is: y=7%2F17









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

So our answers are:

x=12%2F17 and y=7%2F17

which form the ordered pair