Question

Solve for x, y, and z in terms of a, b, and c. {ax+by+cz =a-b+c {bx+by+cz =c {cx+c y+cz=c

Answer 1

To solve the system of equations, use substitution to find x, y, and z in terms of a, b, and c. The solutions are x = (a - b + c - by + cz)/b, y = (c - cx + cz)/c, and z = (a - b + c - ax + b(cx - cz)/c)/(-a - c).

Step-by-step explanation:

To solve the system of equations:

ax + by + cz = a - b + c

bx + by + cz = c

cx + cy + cz = c

1. First, we can simplify the equations by rearranging them:
2. Subtracting c from each side of the first equation, we have ax + by + (c - cz) = a - b
3. Subtracting c from each side of the second equation, we have bx + by + (c - cz) = 0
4. Subtracting c from each side of the third equation, we have cx + cy + (c - cz) = 0
5. Now, we can combine like terms:
6. The first equation becomes ax + by - cz = a - b + c
7. The second equation becomes bx + by - cz = -c
8. The third equation becomes cx + cy - cz = -c
9. Now, using substitution, we can solve for x, y, and z:
10. From the second equation, we have bx + by - cz = -c. Solving for x, we get x = (-c - by + cz)/b
11. Substituting this x value into the first equation, we get a((-c - by + cz)/b) + by - cz = a - b + c
12. Simplifying this equation, we get x = (a - b + c - by + cz)/b
13. Similarly, substituting the x value into the third equation, we get cx + cy - cz = -c
14. Simplifying this equation, we get y = (c - cx + cz)/c
15. Finally, substituting the y value into the first equation, we get ax + b((c - cx + cz)/c) - cz = a - b + c
16. Simplifying this equation, we get z = (a - b + c - ax + b(cx - cz)/c)/(-a - c)