SOLUTION: solve the following by elimination method if there is infinite answers then state that. 5x+5y=50 and 10x+6y=84. I am having trouble with this one since there is no same number in

Algebra ->  Equations -> SOLUTION: solve the following by elimination method if there is infinite answers then state that. 5x+5y=50 and 10x+6y=84. I am having trouble with this one since there is no same number in      Log On


   

Question 466470: solve the following by elimination method if there is infinite answers then state that. 5x+5y=50 and 10x+6y=84. I am having trouble with this one since there is no same number in both.

Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
5x+%2B5y+=+50
10x+%2B+6y+=84
If there are not equal coefficients, then you have to change equation so that there are.
Notice 5 and 10 are multiples of each other.
Also all the coefficients in 2nd equation are divisible by 2.
Divide 2nd equation by -2, *negative because i want equal but opposite numbers*
5x+%2B5y+=+50
-5x+-3y+=+-42
Now the x coefficients are equal but opposite so if I add them together they will become zero.
Add equations together
2y+=+8
Divide by 2 on both sides
y+=+4
Substitute this value into a equation to solve for x:
5x+%2B+5%284%29+=+50
5x+%2B+20+=+50
Subtract 20 on both sides
5x+=+30
Divide by 5 on both sides
x+=+6
Solution is x=6, y=4
Or as a coordinate point:(6,4)