SOLUTION: Hi, Please Solve the systems of equations. 2x+Y=3 4x+3Y=1 Thank you!

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Question 148146: Hi,
Please Solve the systems of equations.
2x+Y=3
4x+3Y=1
Thank you!
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%282x%2By=3%2C4x%2B3y=1%29


-2%282x%2By%29=-2%283%29 Multiply the both sides of the first equation by -2.


-4x-2y=-6 Distribute and multiply.


So we have the new system of equations:
system%28-4x-2y=-6%2C4x%2B3y=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:


%28-4x-2y%29%2B%284x%2B3y%29=%28-6%29%2B%281%29


%28-4x%2B4x%29%2B%28-2y%2B3y%29=-6%2B1 Group like terms.


0x%2By=-5 Combine like terms. Notice how the x terms cancel out.


y=-5 Simplify.


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


-4x-2y=-6 Now go back to the first equation.


-4x-2%28-5%29=-6 Plug in y=-5.


-4x%2B10=-6 Multiply.


-4x=-6-10 Subtract 10 from both sides.


-4x=-16 Combine like terms on the right side.


x=%28-16%29%2F%28-4%29 Divide both sides by -4 to isolate x.


x=4 Reduce.


So our answer is x=4 and y=-5.


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 2x%2By=3 (red) and 4x%2B3y=1 (green)