SOLUTION: 5. 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 a

Algebra ->  Linear-equations -> SOLUTION: 5. 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 a      Log On


   

Question 144716: 5. 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 + 5y = 4
2x – 5y = 2


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%2B5y=4%2C2x-5y=2%29




2%28x%2B5y%29=2%284%29 Multiply the top equation (both sides) by 2
-1%282x-5y%29=-1%282%29 Multiply the bottom equation (both sides) by -1




Distribute and multiply

2x%2B10y=8
-2x%2B5y=-2


Now add the equations together. In order to add 2 equations, group like terms and combine them

%282x-2x%29%2B%2810y%2B5y%29=8-2

Combine like terms and simplify



cross%282x-2x%29%2B15y=6 Notice how the x terms cancel out




15y=6 Simplify




y=6%2F15 Divide both sides by 15 to isolate y




y=2%2F5 Reduce



Now plug this answer into the top equation x%2B5y=4 to solve for x

x%2B5y=4 Start with the first equation



x%2B5%282%2F5%29=4 Plug in y=2%2F5




x%2B10%2F5=4 Multiply




x%2B2=4 Reduce



x=4-2Subtract 2 from both sides


x=2 Combine like terms on the right side




So our answer is
x=2 and y=2%2F5



which form the ordered pair