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.
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.
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.