SOLUTION: Solve by substitution or elimination method: 1. 3x - 2y = 8 -12x + 88 = 32 2. 7x - 5y = 14 -4x + y = 27 3. -4x + 3y = 5 12x - 9y = -15

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Question 153187: Solve by substitution or elimination method:
1. 3x - 2y = 8
-12x + 88 = 32
2. 7x - 5y = 14
-4x + y = 27
3. -4x + 3y = 5
12x - 9y = -15
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
I'll do the first two to get you started:


1)


Start with the given system of equations:




Let's use substitution to solve the system


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

Start with the first equation


Subtract from both sides


Rearrange the equation


Divide both sides by


Break up the fraction


Reduce



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

Since , we can now replace each in the second equation with to solve for



Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.



Distribute to


Multiply


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)



Distribute and multiply the LCM to each side



Combine like terms on the left side


Add 64 to both sides


Combine like terms on the right side


Simplify

Since this equation is never true for any x value, this means there are no solutions.





2)





Start with the given system of equations:




Let's use elimination to solve the system


Multiply the both sides of the second equation by 5.


Distribute and multiply.


So we have the new system of equations:



Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:





Group like terms.


Combine like terms. Notice how the y terms cancel out.


Simplify.


Divide both sides by to isolate .


Reduce.


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


Now go back to the first equation.


Plug in .


Multiply.


Add to both sides.


Combine like terms


Divide both sides by -5.




So our answer is and .


Which form the ordered pair .



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