SOLUTION: Solve this system using the Substitution Method: x + y = 7/2 4x - 3y = -14

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Question 196595: Solve this system using the Substitution Method:
x + y = 7/2
4x - 3y = -14
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x+%2B+y+=+7%2F2 Start with the first equation.


2x%2B2y=7 Multiply every term by 2 to clear out the fraction.



So we have the system of equations:

system%282x%2B2y=7%2C4x-3y=-14%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%2B2y=7 Start with the first equation


2y=7-2x Subtract 2x from both sides


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


y=%28-2x%2B7%29%2F%282%29 Divide both sides by 2


y=%28%28-2%29%2F%282%29%29x%2B%287%29%2F%282%29 Break up the fraction


y=-x%2B7%2F2 Reduce



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

Since y=-x%2B7%2F2, we can now replace each y in the second equation with -x%2B7%2F2 to solve for x



4x-3highlight%28%28-x%2B7%2F2%29%29=-14 Plug in y=-x%2B7%2F2 into the second equation. In other words, replace each y with -x%2B7%2F2. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



4x%2B%28-3%29%28-1%29x%2B%28-3%29%287%2F2%29=-14 Distribute -3 to -x%2B7%2F2


4x%2B3x-21%2F2=-14 Multiply


%282%29%284x%2B3x-21%2F2%29=%282%29%28-14%29 Multiply both sides by the LCM of 2. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



8x%2B6x-21=-28 Distribute and multiply the LCM to each side



14x-21=-28 Combine like terms on the left side


14x=-28%2B21Add 21 to both sides


14x=-7 Combine like terms on the right side


x=%28-7%29%2F%2814%29 Divide both sides by 14 to isolate x



x=-1%2F2 Reduce





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


So the first part of our answer is: x=-1%2F2









Since we know that x=-1%2F2 we can plug it into the equation y=-x%2B7%2F2 (remember we previously solved for y in the first equation).



y=-x%2B7%2F2 Start with the equation where y was previously isolated.


y=-%28-1%2F2%29%2B7%2F2 Plug in x=-1%2F2


y=1%2F2%2B7%2F2 Multiply


y=4 Combine like terms and reduce.


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


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









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

So our answers are:

x=-1%2F2 and y=4

which form the ordered pair