SOLUTION: 3x-5y=11 x-3y=1

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Question 179036This question is from textbook glencoe mathematics
: 3x-5y=11
x-3y=1 This question is from textbook glencoe mathematics

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%283x-5y=11%2Cx-3y=1%29


-3%28x-3y%29=-3%281%29 Multiply the both sides of the second equation by -3.


-3x%2B9y=-3 Distribute and multiply.


So we have the new system of equations:
system%283x-5y=11%2C-3x%2B9y=-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%2B9y%29=%2811%29%2B%28-3%29


%283x%2B-3x%29%2B%28-5y%2B9y%29=11%2B-3 Group like terms.


0x%2B4y=8 Combine like terms.


4y=8 Simplify.


y=%288%29%2F%284%29 Divide both sides by 4 to isolate y.


y=2 Reduce.


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3x-5y=11 Now go back to the first equation.


3x-5%282%29=11 Plug in y=2.


3x-10=11 Multiply.


3x=11%2B10 Add 10 to both sides.


3x=21 Combine like terms on the right side.


x=%2821%29%2F%283%29 Divide both sides by 3 to isolate x.


x=7 Reduce.


So our answer is x=7 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 3x-5y=11 (red) and x-3y=1 (green)