Question

What is the equation you get whenever you combine the top 2 equations:

x + 4y – 3z = -7
2x – 4y + 4z = 2
-6x + 4y + 4z = -14
A) x - 5y + z = -5
B) x + 5y + z = -5
C) x - 5y + z = -2
D) x + 5y + z = -2

Answer 1

By adding the top two equations x + 4y – 3z = -7 and 2x – 4y + 4z = 2, we can eliminate y and obtain the simplified equation 3x + z = -5. Dividing by 3 gives us x + z/3 = -5/3, which doesn't match any of the provided options, suggesting a mistake in the question or the given answers.

Step-by-step explanation:

To combine the top two equations x + 4y – 3z = -7 and 2x – 4y + 4z = 2, we can add them together because they are set up perfectly for elimination of the variable y. When we add them, the 4y and –4y cancel each other out, giving us:

x + 4y – 3z + 2x – 4y + 4z = -7 + 2

This simplifies to:

3x + z = -5

Dividing everything by 3 to solve for x, we get:

x + z/3 = -5/3

This is not one of the provided options, which suggests there might be an error in the options given or in the process of combining the equations. If we check the options provided in the question against this result, none match precisely, indicating a potential mistake in the question or the answers provided. However, it is important to correctly execute the steps of combining equations using elimination or substitution to draw conclusions about the existence of potential errors.