Question

Solve the system using a matrix: -x - y - z = -19, 4y + 4z = 4, 2x + y + 6z = 7. If x = -4, what is the solution as an ordered triple (x, y, z)?

a) (-4, 5, -2)
b) (-4, -2, 5)
c) (-4, 1, 4)
d) (-4, 4, 1)

Answer 1

After substituting x = -4 into the third equation, we solve for y and z to find that the ordered triple is (-4, -1.8, 2.8), which does not match any of the provided options.

Step-by-step explanation:

To solve the system of equations:

• -x - y - z = -19,
• 4y + 4z = 4,
• 2x + y + 6z = 7,

using a matrix and given that x = -4, we can substitute x into the third equation to find the values of y and z.

Substituting x = -4 into the third equation:

2(-4) + y + 6z = 7 → -8 + y + 6z = 7 → y + 6z = 15

Now we have two equations with two variables:

• 4y + 4z = 4,
• y + 6z = 15.

We can simplify the first equation by dividing everything by 4:

y + z = 1

Now we have a system of two equations:

• y + z = 1,
• y + 6z = 15.

Subtract the first equation from the second to eliminate y:

(y + 6z) - (y + z) = 15 - 1 → 5z = 14 → z = 14/5 = 2.8

Now back-substitute the value of z into y + z = 1 to find y:

y + 2.8 = 1 → y = 1 - 2.8 → y = -1.8

Therefore, the solution as an ordered triple is (-4, -1.8, 2.8).

However, since none of the provided options match this result, we may need to check if there is a mistake or if the question or the given options are incorrect.