SOLUTION: solve each system by any method 1 x-3y=1 3x-5y=-5 2 2x-3y=5 4x-6y=3

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Question 168732: solve each system by any method
1 x-3y=1
3x-5y=-5
2 2x-3y=5
4x-6y=3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

Substitution:

x-3y=1 Start with the first equation


x=3y%2B1 Add 3y to both sides.


3x-5y=-5 Move onto the second equation


3%283y%2B1%29-5y=-5 Plug in x=3y%2B1


9y%2B3-5y=-5 Distribute.


4y%2B3=-5 Combine like terms on the left side.


4y=-5-3 Subtract 3 from both sides.


4y=-8 Combine like terms on the right side.


y=%28-8%29%2F%284%29 Divide both sides by 4 to isolate y.


y=-2 Reduce.


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

x=3y%2B1 Go back to the first isolated equation


x=3%28-2%29%2B1 Plug in y=-2


x=-6%2B1 Multiply


x=-5 Add



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So the solutions are x=-5 and y=-2 which form the ordered pair (-5, -2)






# 2

Elimination:




Start with the given system of equations:
system%282x-3y=5%2C4x-6y=3%29


-2%282x-3y%29=-2%285%29 Multiply the both sides of the first equation by -2.


-4x%2B6y=-10 Distribute and multiply.


So we have the new system of equations:
system%28-4x%2B6y=-10%2C4x-6y=3%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:


%28-4x%2B6y%29%2B%284x-6y%29=%28-10%29%2B%283%29


%28-4x%2B4x%29%2B%286y%2B-6y%29=-10%2B3 Group like terms.


0x%2B0y=-7 Combine like terms. Notice how the x terms cancel out.


0=-7Simplify.


Since 0=-7 is never true, this means that there are no solutions. So the system is inconsistent.