I'm extremely confused with these two problems:
What would I do first... would I subtract or add? I don't know when I should subtract or when I should add.
would I add for this one?
Use Gaussian elimination with row operations to find g. Then back substituting the answer for g into equation one to solve for f.
first multiply equation 2 by -1.
then add equation 1 and equation 2. the sum is the new equation 2
multiply equation 2 by 1/5.
now back substitute g into equation 1 and solve for f.
The first step in know what to do is understanding why you would want to do it! You object is to eliminate one of the unknown letters. You should see that the coefficient of "f" in both equations is "7". Subtracting will give 7f- 7f= 0 which eliminates "f". Adding them would not.
For 5m- p= 7, 7m- p= 11, p has coefficient -11 in both equations. Subtracting will give -11p- (-11p)= 0.
would I add for this one?
Notice that skoker multiplied an equation by -1 and then added. Of course, that is the same as subtracting the equations.
Whichever happens to be simplest to eliminate.
For the first problem,
5m- p= 7
7m- p= 11
You can see that each p has a "coefficient" of -1. If we simply subtract the second equation from the first equation, those will cancel: (5m- 7m)- (p- p)= 7- 11 or -2m= 4. Or subtract the first equation from the first, if you don't like negative numbers: (7m- 5m)- (p- p)= 11- 7 or 2m= 4. Once you have found that m= 2, put that back into either equation: 5(2)- p= 7 so that 10- p= 7 and p= 3.
But I could have multiplied each part of the first equation by 7 to get 35m- 7p= 49 and multiplied each part of the second equation by 5 to get 35m- 5p= 55 so that now the each m has the same coefficient, 35. If I subtract the second equation from the first, I get (35m- 35m)- (7p- 5p)= 49- 55 or 2p= 6 so that p= 3. Put that back into either of the first equations: 5m- (3)= 7, 5m= 7+ 3= 10, m= 2.