SOLUTION: in solving the following equation the book says to multiply by 10 but it does not explain why we are only multiplying the second equation by ten and it does not explain where we pu

Question 479366: in solving the following equation the book says to multiply by 10 but it does not explain why we are only multiplying the second equation by ten and it does not explain where we pulled the 10 from. I understand that in an equation such as 2x-y=6 and 4x-2y=1 that I would only multiply equation number 1 by (-2) so that my final answer would be 0=11 which is inconsistent. However the on-line class and textbook neither one gives and explanation as to where they are getting the multiplier from for the following two examples. could you please explain these to me. If I know why and where they got the multiplier I can solve problems like these in the future. the two equations are
x+0.4y=3.08
0.1x-y=0.1
the book says to multiply only the second equation by 10. Why?
the other one is
-4x+y=-2
8x-2y=4
The book says to multiply the second equation by one half (1/2) again why and where did they get 1/2 from. Thank you for your help
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
to solve a system of equations by ELIMINATION, you have to get equal value coefficients for the term to be eliminated
___ the multiplier is the ratio of the coefficients

in the 1st pair, multiplying the 2nd equation by 10 makes the x-term coefficients equal
___ subtracting the equations eliminates the x's

in the 2nd pair, multiplying the 2nd equation by 1/2 makes ALL the terms equal but opposite
___ this indicates that the equations are essentially the same, with an infinite number of solutions
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