SOLUTION: I need to know if my answer is correct for the following: If it isn't, I need to know why. thanks Solve the system of equations x+2y=1 3x-2y=11 My answer is (3,-1) Thank you

Algebra ->  Rectangles -> SOLUTION: I need to know if my answer is correct for the following: If it isn't, I need to know why. thanks Solve the system of equations x+2y=1 3x-2y=11 My answer is (3,-1) Thank you       Log On


   

Question 218289: I need to know if my answer is correct for the following: If it isn't, I need to know why. thanks
Solve the system of equations
x+2y=1
3x-2y=11
My answer is (3,-1)
Thank you very much!
Found 2 solutions by jim_thompson5910, solver91311:
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%2B2y=1%2C3x-2y=11%29


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%283x-2y%29=%281%29%2B%2811%29


%281x%2B3x%29%2B%282y%2B-2y%29=1%2B11 Group like terms.


4x%2B0y=12 Combine like terms. Notice how the y terms cancel out.


4x=12 Simplify.


x=%2812%29%2F%284%29 Divide both sides by 4 to isolate x.


x=3 Reduce.


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


x%2B2y=1 Now go back to the first equation.


3%2B2y=1 Plug in x=3.


3%2B2y=1 Multiply.


2y=1-3 Subtract 3 from both sides.


2y=-2 Combine like terms on the right side.


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


y=-1 Reduce.


So our answer is x=3 and y=-1.


Which form the ordered pair . Good job. As a check, simply plug in x=3 and y=-1 and you should get two identities.


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=1 (red) and 3x-2y=11 (green)

Answer by solver91311(24713) About Me  (Show Source):