Answer:
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
therefore, the statement (-4, 6, 3) is correct.
