Need Help! 50 points!!

see below

Step-by-step explanation:

eq.1      2a   - b + 2c = -8

eq.2            5b  - 3c =  21

eq.3     -7a        -10c = -2

3 equations, 3 unknown.

first step is to eliminate b using eq1 and eq2

2a   - b + 2c = -8 (5)

      5b  - 3c =  21

10a - 5b + 10c = -40

        5b -  3c =  21

10a        + 7c = -21 eq. A

lets solve a using eq. A

10a + 7c = -21

a = (-7c - 21) / 10

now substitute a into eq.3

-7a        -10c = -2

-7(-7c - 21) -10c = -2 distribute

        10

4.9c + 14.7 - 10c = -2  add similar terms

-5.1c = -2 - 14.7  simplify

c = -16.7 / -5.1

c  ≈ 3

solve b using eq. 2 and substitute c.

5b  - 3c =  21

5b = 21 + 3c

5b = 21 + 3(3.2)

b = 30.825 / 5

b ≈ 6

solve a using eq. A

10a + 7c = -21

10a + 7(3.2) = -21

10a = -21 - 22.4

a = -43.4 / 10

a ≈ -4