Question

Solve the system of equations:

x = 8 + t * 2 - t * 1
y = -13 + t * 1 - t * 0
z = -6 + t * 3 - t * 0

Answer 1

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.