SOLUTION: Solve the system of equations using the addition (elimination) method. If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answe

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve the system of equations using the addition (elimination) method. If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answe      Log On


   

Question 154341: Solve the system of equations using the addition (elimination) method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no solution” or “infinitely many solutions.”
x + 2y = 5
3x + 4y = 1
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=5%2C3x%2B4y=1%29


-2%28x%2B2y%29=-2%285%29 Multiply the both sides of the first equation by -2.


-2x-4y=-10 Distribute and multiply.


So we have the new system of equations:
system%28-2x-4y=-10%2C3x%2B4y=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:


%28-2x-4y%29%2B%283x%2B4y%29=%28-10%29%2B%281%29


%28-2x%2B3x%29%2B%28-4y%2B4y%29=-10%2B1 Group like terms.


x%2B0y=-9 Combine like terms. Notice how the y terms cancel out.


x=-9 Simplify.


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-2x-4y=-10 Now go back to the first equation.


-2%28-9%29-4y=-10 Plug in x=-9.


18-4y=-10 Multiply.


-4y=-10-18 Subtract 18 from both sides.


-4y=-28 Combine like terms on the right side.


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


y=7 Reduce.


So our answer is x=-9 and y=7.


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%2B2y=5 (red) and 3x%2B4y=1 (green)