SOLUTION: Please Help. Use elimination to solve each system of equations. X+4Y=11 X-6Y=11

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Question 182608: Please Help.
Use elimination to solve each system of equations.
X+4Y=11 X-6Y=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%2B4y=11%2Cx-6y=11%29


-1%28x%2B4y%29=-1%2811%29 Multiply the both sides of the first equation by -1.


-x-4y=-11 Distribute and multiply.


So we have the new system of equations:
system%28-x-4y=-11%2Cx-6y=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:


%28-x-4y%29%2B%28x-6y%29=%28-11%29%2B%2811%29


%28-x%2Bx%29%2B%28-4y%2B-6y%29=-11%2B11 Group like terms.


0x%2B-10y=0 Combine like terms.


-10y=0 Simplify.


y=%280%29%2F%28-10%29 Divide both sides by -10 to isolate y.


y=0 Reduce.


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-x-4y=-11 Now go back to the first equation.


-x-4%280%29=-11 Plug in y=0.


-x%2B0=-11 Multiply.


-x=-11 Remove any zero terms.


x=%28-11%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=11 Reduce.


So our answer is x=11 and y=0.


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%2B4y=11 (red) and x-6y=11 (green)