SOLUTION: Can someone show me how to use the elimination method to solve this problem. The solution says it is (4y+1,y) for any real numbers. I just don't kow how they go it. Thanks 2x

Algebra ->  Matrices-and-determiminant -> SOLUTION: Can someone show me how to use the elimination method to solve this problem. The solution says it is (4y+1,y) for any real numbers. I just don't kow how they go it. Thanks 2x      Log On


   

Question 332233: Can someone show me how to use the elimination method to solve this problem. The solution says it is (4y+1,y) for any real numbers. I just don't kow how they go it. Thanks
2x-8y=2
3x-12y=3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
It turns out that this system has an infinite number of solutions. Basically one equation is just the other in a different form. So to solve this "system", we just need to solve for one variable. So what the book did was solve for 'y' (in either equation).


So take 2x-8y=2 and solve for x to get 2x=8y%2B2 ----> x=%288y%2B2%29%2F2 ----> x=4y%2B1


So every 'x' coordinate of the solution is simply equal to 4 times the y coordinate plus one.


So recall that any solution of a system is of the form (x,y) and we know that x=4y%2B1, this means that the solution is (4y+1,y)



Note: there are other ways to display the solution, but you essentially get the same thing.