Question

Solve the system of equations.
x-y + 9z = -27
2x – 4y - z= -1
3x + 6y - 3z = 27

Answer 1

To solve the system of equations x - y + 9z = -27, 2x - 4y - z = -13, and x + 6y - 3z = 27, we can use the method of elimination or substitution. After performing the necessary operations, the solution to the system of equations is x = -4, y = -9/4, and z = 1/4.

Step-by-step explanation:

To solve the system of equations x - y + 9z = -27, 2x - 4y - z = -13, and x + 6y - 3z = 27, we can use the method of elimination or substitution. Let's use the method of elimination:

1. Multiply the first equation by 2 to make the coefficients of x in the first and second equations the same, yielding 2x - 2y + 18z = -54.
2. Subtract the second equation from the first equation to eliminate x, resulting in -y + 19z = -41.
3. Multiply the first equation by 3 to make the coefficients of x in the first and third equations the same, giving us 3x - 3y + 27z = 81.
4. Subtract the third equation from the first equation to eliminate x, giving us -9y + 36z = -54.
5. Multiply the second equation by 3 to make the coefficients of y in the second and third equations the same, resulting in 6x - 12y - 3z = -39.
6. Subtract the third equation from the second equation to eliminate y, yielding 5y - 4z = -36.
7. Now, we have a system of two equations: -y + 19z = -41 and 5y - 4z = -36.
8. Multiply the second equation by -1 to make the coefficients of y in the two equations the same, resulting in y - 19z = 36.
9. Add the first equation to the second equation to eliminate y, giving us -20z = -5.
10. Divide both sides of the equation by -20 to solve for z, resulting in z = 1/4.
11. Substitute the value of z back into one of the original equations to solve for y and x.

Therefore, the solution to the system of equations is x = -4, y = -9/4, and z = 1/4.