1). A + C - 2E = 2
2). A - 2C = 5
3). - C + E = 4
Use 2). and 3) to solve for A in 2). and E in 3).
2a). A - 2C = 5, A = 2C + 5
3a). -C + E = 4
3a). E = C + 4
substitute into 1).
1). A + C - 2E = 2
1a). 2C + 5 + C -2(C + 4) = 2
1a). 3C + 5 - 2C - 8 = 2
1a). C - 3 = 2
1a). C = 5
substitute C = 5 into the orginal equations.
1). A + C - 2E = 2 1b). A + 5 - 2E = 2
1b). A - 2E = -3
2). A - 2C = 5 2b). A - 2*5 = 5
2b). A = 15
3). - C + E = 4 3b). -5 + E = 4
3b). E = 9
so A = 15, C = 5 and E = 9
CHECK:
1). A + C - 2E = 2, A = 15, C = 5 and E = 9
15 + 5 - 2*9 = 2
20 -18 = 2
2 = 2 checks.
2). A - 2C = 5, A = 15, C = 5 and E = 9
15 - 2*5 = 5
15 - 10 = 5
5 = 5 checks
3). - C + E = 4, A = 15, C = 5 and E = 9
-5 + 9 = 4
4 = 4 checks
A = 15, C = 5 and E = 9 is the solution.