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

Algebra ->  Coordinate Systems and Linear Equations -> 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      Log On


   

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) About Me  (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:

system%283x-2y=8%2C-12x%2B8y=32%29


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

3x-2y=8 Start with the first equation


-2y=8-3x Subtract 3x from both sides


-2y=-3x%2B8 Rearrange the equation


y=%28-3x%2B8%29%2F%28-2%29 Divide both sides by -2


y=%28%28-3%29%2F%28-2%29%29x%2B%288%29%2F%28-2%29 Break up the fraction


y=%283%2F2%29x-4 Reduce



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Since y=%283%2F2%29x-4, we can now replace each y in the second equation with %283%2F2%29x-4 to solve for x



-12x%2B8highlight%28%28%283%2F2%29x-4%29%29=32 Plug in y=%283%2F2%29x-4 into the first equation. In other words, replace each y with %283%2F2%29x-4. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



-12x%2B%288%29%283%2F2%29x%2B%288%29%28-4%29=32 Distribute 8 to %283%2F2%29x-4


-12x%2B%2824%2F2%29x-32=32 Multiply


%282%29%28-12x%2B%2824%2F2%29x-32%29=%282%29%2832%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)



-24x%2B24x-64=64 Distribute and multiply the LCM to each side



-64=64 Combine like terms on the left side


0=64%2B64Add 64 to both sides


0=128 Combine like terms on the right side


0=128 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:
system%287x-5y=14%2C-4x%2By=27%29



Let's use elimination to solve the system


5%28-4x%2By%29=5%2827%29 Multiply the both sides of the second equation by 5.


-20x%2B5y=135 Distribute and multiply.


So we have the new system of equations:
system%287x-5y=14%2C-20x%2B5y=135%29


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


%287x-5y%29%2B%28-20x%2B5y%29=%2814%29%2B%28135%29


%287x%2B-20x%29%2B%28-5y%2B5y%29=14%2B135 Group like terms.


-13x%2B0y=149 Combine like terms. Notice how the y terms cancel out.


-13x=149 Simplify.


x=%28149%29%2F%28-13%29 Divide both sides by -13 to isolate x.


x=-149%2F13 Reduce.


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


7x-5y=14 Now go back to the first equation.


7%28-149%2F13%29-5y=14 Plug in x=-149%2F13.


-1043%2F13-5y=14 Multiply.


-5y=14%2B1043%2F13 Add 1043%2F13 to both sides.


-5y=1225%2F13 Combine like terms


y=-245%2F13 Divide both sides by -5.




So our answer is x=-149%2F13 and y=-245%2F13.


Which form the ordered pair .