SOLUTION: Solve each system using the indicated method. State wheather the system is consistent or inconsistent and dependent or independent. Must use the addition method. A. x+2y=7

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Question 164076: Solve each system using the indicated method. State wheather the system is consistent or inconsistent and dependent or independent. Must use the addition method.
A. x+2y=7
x-y=1
B. 3x-5y=5
-x+y=-1
C. 7x-4y=27
5x+6y=6
D. 2x+3y=8
3x+3y=12
If someone can help me solve one of these, then i can build off of it to hopefully complete the other ones. Thanks and please help
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

A)



Start with the given system of equations:
system%28x%2B2y=7%2Cx-y=1%29


-1%28x-y%29=-1%281%29 Multiply the both sides of the second equation by -1. Doing so will make the coefficients of the two x terms be equal but opposite.


-x%2By=-1 Distribute and multiply.


So we have the new system of equations:
system%28x%2B2y=7%2C-1x%2By=-1%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:


%28x%2B2y%29%2B%28-1x%2By%29=%287%29%2B%28-1%29


%28x-x%29%2B%282y%2By%29=7%2B-1 Group like terms.


0x%2B3y=6 Combine like terms. Notice how the x terms cancel out.


3y=6 Simplify.


y=%286%29%2F%283%29 Divide both sides by 3 to isolate y.


y=2 Reduce.


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


x%2B2y=7 Now go back to the first equation.


x%2B2%282%29=7 Plug in y=2.


x%2B4=7 Multiply.


x=7-4 Subtract 4 from both sides.


x=3 Combine like terms on the right side.


So our answer is x=3 and y=2.


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of x%2B2y=7 (red) and x-y=1 (green)




B)



Start with the given system of equations:
system%283x-5y=5%2C-x%2By=-1%29


3%28-x%2By%29=3%28-1%29 Multiply the both sides of the second equation by 3.


-3x%2B3y=-3 Distribute and multiply.


So we have the new system of equations:
system%283x-5y=5%2C-3x%2B3y=-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:


%283x-5y%29%2B%28-3x%2B3y%29=%285%29%2B%28-3%29


%283x%2B-3x%29%2B%28-5y%2B3y%29=5%2B-3 Group like terms.


0x%2B-2y=2 Combine like terms. Notice how the x terms cancel out.


-2y=2 Simplify.


y=%282%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=-1 Reduce.


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


3x-5y=5 Now go back to the first equation.


3x-5%28-1%29=5 Plug in y=-1.


3x%2B5=5 Multiply.


3x=5-5 Subtract 5 from both sides.


3x=0 Combine like terms on the right side.


x=%280%29%2F%283%29 Divide both sides by 3 to isolate x.


x=0 Reduce.


So our answer is x=0 and y=-1.


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of 3x-5y=5 (red) and -x%2By=-1 (green)