Final answer:
To solve the given system of equations, substitution or elimination methods can be used. By substituting the second equation into the first, solving for y, and then substituting back to find z and x, the solution is found to be x = 4, y = 1, z = -1.
Step-by-step explanation:
The question asks to find the solution to the system of equations:
2x - 3y = 5
x + 2z = 2
y - 4z = -11
To solve this, we can use a method such as substitution or elimination. Here's a step-by-step example using substitution:
Solve the second equation for x: x = 2 - 2z.
Substitute x into the first equation: 2(2 - 2z) - 3y = 5 which simplifies to 4 - 4z - 3y = 5.
Rearrange the simplified equation to solve for y: -3y = 4z + 1.
Substitute the expression for y into the third equation: (-4z - 1)/-3 - 4z = -11, simplifying gives z = -1.
Substitute z into the equation solved for y: y = (-4(-1) - 1)/-3, which gives y = 1.
Substitute z into the equation solved for x: x = 2 - 2(-1), which gives x = 4.
Therefore, the solution to the system is x = 4, y = 1, z = -1.