Question

Solve the system of equations using any method.

b. (x + y + z = 7)
c. (x - 8y - z = -29)
d. (4x - y + z = 8)

Answer 1

To solve the system of equations x + y + z = 7, x - 8y - z = -29, and 4x - y + z = 8, we can use the elimination method. The solution to the system of equations is x = -1, y = 4, and z = 4.

Step-by-step explanation:

To solve the system of equations x + y + z = 7, x - 8y - z = -29, and 4x - y + z = 8, we can use the elimination method. Here are the steps:

1. Add the second and third equations together to eliminate z. This gives us x - 8y - z + 4x - y + z = -29 + 8, which simplifies to 5x - 9y = -21.
2. Add the first and second equations together to eliminate z. This gives us x + y + z + x - 8y - z = 7 + (-29), which simplifies to 2x - 7y = -22.
3. Now we have a system of two equations: 5x - 9y = -21 and 2x - 7y = -22. We can solve this system using any method such as substitution or elimination.
4. Let's use substitution. Solve one equation for one variable and substitute it into the other equation. Let's solve the second equation for x: x = (7y - 22) / 2.
5. Substitute this expression for x into the first equation: 5((7y - 22) / 2) - 9y = -21. Simplify this equation to get 35y - 110 - 18y = -42, which simplifies further to 17y = 68.
6. Divide both sides of the equation by 17 to solve for y: y = 4.
7. Substitute this value of y back into the second equation to solve for x: x = (7(4) - 22) / 2. Simplify this expression to get x = -1.
8. Substitute the values of x and y into any of the original equations to solve for z. Let's use the first equation: -1 + 4 + z = 7. Simplify this equation to get z = 4.

The solution to the system of equations is x = -1, y = 4, and z = 4.