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.