Question

Solve the system of equations for (x, y, z) and choose the correct solution

3x + 3y - 2z = 14,x - 6z = 16,2x + 5z = -2.

A) x = 5, y = -3, z = -2.
B) x = 2, y = 4, z = -1.
C) x = 7, y = -1, z = 3.
D) x = -1, y = 6, z = 4.

Answer 1

To solve the system of equations: 3x + 3y - 2z = 14, x - 6z = 16, 2x + 5z = -2, you can use the method of substitution or elimination. Using the method of substitution, the solution is x = 4, y = -3, and z = -2.

Step-by-step explanation:

To solve the system of equations:

3x + 3y - 2z = 14

x - 6z = 16

2x + 5z = -2

We can use the method of substitution or elimination to find the values of x, y, and z.

Using the method of substitution, we can solve the second equation for x:

x = 16 + 6z

Substituting this value in the other two equations:

3(16 + 6z) + 3y - 2z = 14

2(16 + 6z) + 5z = -2

Simplifying these equations, we get:

48 + 18z + 3y - 2z = 14

32 + 12z + 5z = -2

Combining like terms:

16z + 3y = -34

17z = -34

z = -2

Substituting this value back into the other equations, we can find the values of x and y:

From the second equation: x = 16 + 6(-2) = 4

From the third equation: 2(4) + 5(-2) = -2

So the solution to the system of equations is x = 4, y = -3, and z = -2.