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 ->  Linear-equations -> 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 180714: 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" and state how you arrived at that conclusion.
4x + 10y = 2
3x + 5y = 5
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%284x%2B10y=2%2C3x%2B5y=5%29


-2%283x%2B5y%29=-2%285%29 Multiply the both sides of the second equation by -2.


-6x-10y=-10 Distribute and multiply.


So we have the new system of equations:
system%284x%2B10y=2%2C-6x-10y=-10%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:


%284x%2B10y%29%2B%28-6x-10y%29=%282%29%2B%28-10%29


%284x%2B-6x%29%2B%2810y%2B-10y%29=2%2B-10 Group like terms.


-2x%2B0y=-8 Combine like terms.


-2x=-8 Simplify.


x=%28-8%29%2F%28-2%29 Divide both sides by -2 to isolate x.


x=4 Reduce.


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


4x%2B10y=2 Now go back to the first equation.


4%284%29%2B10y=2 Plug in x=4.


16%2B10y=2 Multiply.


10y=2-16 Subtract 16 from both sides.


10y=-14 Combine like terms on the right side.


y=%28-14%29%2F%2810%29 Divide both sides by 10 to isolate y.


y=-7%2F5 Reduce.


So the solutions are x=4 and y=-7%2F5


Which form the ordered pair .


This means that the system is consistent and independent.