SOLUTION: solve this equation. x+y=1 4x-3y=11

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Question 249039: solve this equation.
x+y=1
4x-3y=11
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%28x%2By=1%2C4x-3y=11%29


3%28x%2By%29=3%281%29 Multiply the both sides of the first equation by 3.


3x%2B3y=3 Distribute and multiply.


So we have the new system of equations:
system%283x%2B3y=3%2C4x-3y=11%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%2B3y%29%2B%284x-3y%29=%283%29%2B%2811%29


%283x%2B4x%29%2B%283y%2B-3y%29=3%2B11 Group like terms.


7x%2B0y=14 Combine like terms.


7x=14 Simplify.


x=%2814%29%2F%287%29 Divide both sides by 7 to isolate x.


x=2 Reduce.


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


3x%2B3y=3 Now go back to the first equation.


3%282%29%2B3y=3 Plug in x=2.


6%2B3y=3 Multiply.


3y=3-6 Subtract 6 from both sides.


3y=-3 Combine like terms on the right side.


y=%28-3%29%2F%283%29 Divide both sides by 3 to isolate y.


y=-1 Reduce.


So the solutions are x=2 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 x%2By=1 (red) and 4x-3y=11 (green)