Final answer:
To solve the system of equations, set the expressions for x, y, and z equal to each other and simplify the resulting equation. Substitute the value of t back into the original equations to find the values of x, y, and z. The solution is x = -22, y = -34, and z = -33.
Step-by-step explanation:
To solve the system of equations:
x = 8 + t * 2 - t * 1
y = -13 + t * 1 - t * 0
z = -6 + t * 3 - t * 0
We can solve this system by setting the expressions for x, y, and z equal to each other.
8 + t * 2 - t * 1 = -13 + t * 1 - t * 0 = -6 + t * 3 - t * 0
Combining like terms and simplifying, we get:
t = -21
Substituting this value of t back into the original equations, we can find the values for x, y, and z:
x = 8 + (-21) * 2 - (-21) * 1 = -22
y = -13 + (-21) * 1 - (-21) * 0 = -34
z = -6 + (-21) * 3 - (-21) * 0 = -33
Therefore, the solution to the system of equations is x = -22, y = -34, and z = -33.