Question

use substitution to solve the following system of equations.
d+e-f=11
e=f+d+5
f=2e-12
ps. if solve you get a medal

Answer 1

solve one of the equations for one of its variables, it doesn't matter which one you chose because there is no incorrect choice...
f = 2e - 12

now substitute the value from the first variable you solved for into any of the other equations and solve for the next variable
e = f + d + 5
e = (2e - 12) + d + 5
e = 2e + d - 7
-e = d - 7
e = -d + 7

now substitute the two variables you have into the last equation...
d + e - f = 11
d + (-d + 7) - (2e - 12) = 11
d - d + 7 - 2e + 12 = 11
19 - 2e = 11
19 - 11 = 2e
8 = 2e
4 = e

now sub 4 in for e...
e = -d + 7
4 = - d + 7
-3 = - d
3 = d

now sub in your known variables into original equation to solve for last variable...
d + e - f = 11
3 + 4 - f = 11
7 - f = 11
-f = 4
f = - 4

now check...
f = 2e - 12
-4 = 2(4) - 12
-4 = 8 - 12
-4 = -4 (correct)

answer : e = 4, f = -4, d = 3

If you have any questions at all about what I did, please ask.
you can also look here....
http://www.mrferrante.com/algebra2/final_review/chapter3/3.6.1.html