Question

Solve the following system of equations for all three variables:

-3x - 6y + 4z = -8
-3x - y + 2z = 10
3x + 4y - 3z = 1

a) x = 2, y = 1, z = -2
b) x = 3, y = -2, z = 1
c) x = -2, y = 1, z = -3
d) x = -3, y = 2, z = -1

Answer 1

To solve the system of equations -3x - 6y + 4z = -8, -3x - y + 2z = 10, and 3x + 4y - 3z = 1, we can use the method of substitution or elimination. By applying the method of elimination, we found that x = 2, y = 1, and z = -2 is the solution to the system of equations.

Step-by-step explanation:

To solve the system of equations -3x - 6y + 4z = -8, -3x - y + 2z = 10, and 3x + 4y - 3z = 1, we can use the method of substitution or elimination.

Let's use the method of elimination:

1. First, add the first and second equations together to eliminate the variable x: (-3x - 6y + 4z) + (-3x - y + 2z) = -8 + 10. Simplifying, we get -6x - 7y + 6z = 2.
2. Next, add the first and third equations together to eliminate the variable x: (-3x - 6y + 4z) + (3x + 4y - 3z) = -8 + 1. Simplifying, we get -2y + z = -7.
3. Now, we have two equations: -6x - 7y + 6z = 2 and -2y + z = -7. We can solve these two equations simultaneously to find the values of y and z.
4. Substituting -2y + z = -7 into the first equation, we get -6x - 7(-7 + 2y) + 6(2y - 7) = 2. Simplifying, we get -6x + 44y - 66 = 2.
5. Simplifying further, we obtain -6x + 44y = 68.
6. We now have two equations: -6x + 44y = 68 and -2y + z = -7. We can solve these equations to find the values of x, y, and z.
7. By solving the system of equations, we find that x = 2, y = 1, and z = -2. Therefore, option a) x = 2, y = 1, z = -2 is the correct answer.