Answer:
I'm not so sure
Explanation:
Let's solve the system of equations again using the given solution.
1) x + ay + cz = 0
Substituting x = 3, y = -1, z = 2:
3 + a(-1) + c(2) = 0
3 - a + 2c = 0
- a + 2c = -3 ---(Equation 1)
2) bx + cy - 3z = 1
Substituting x = 3, y = -1, z = 2:
b(3) + c(-1) - 3(2) = 1
3b - c - 6 = 1
3b - c = 7 ---(Equation 2)
3) ax + 2y + bz = 25
Substituting x = 3, y = -1, z = 2:
a(3) + 2(-1) + b(2) = 25
3a - 2 + 2b = 25
3a + 2b = 27 ---(Equation 3)
To solve this system, we can use the method of substitution.
From Equation 1, we can express a in terms of c:
- a + 2c = -3
a = 2c - 3
Substitute this value of a in Equation 3:
3a + 2b = 27
3(2c - 3) + 2b = 27
6c - 9 + 2b = 27
6c + 2b = 36 ---(Equation 4)
Now we have two equations with two variables, Equation 2 and Equation 4:
3b - c = 7 ---(Equation 2)
6c + 2b = 36 ---(Equation 4)
We can solve this system of equations to find the values of b and c.
Multiplying Equation 2 by 2, we get:
6b - 2c = 14
Adding this equation to Equation 4, we eliminate c:
6c + 2b + 6b - 2c = 36 + 14
8b = 50
b = 50/8
b = 6.25
Substituting the value of b back into Equation 2, we can solve for c:
3(6.25) - c = 7
18.75 - c = 7
-c = 7 - 18.75
-c = -11.75
c = 11.75
Now that we have the values of b and c, we can substitute them into Equation 1 to solve for a:
- a + 2(11.75) = -3
- a + 23.5 = -3
- a = -3 - 23.5
- a = -26.5
a = 26.5
Finally, we can calculate the value of a + b + c:
a + b + c = 26.5 + 6.25 + 11.75
a + b + c = 44.5
Therefore, a + b + c is equal to 44.5.