Question

Solve the following system of equations for all three variables.

7x−3y+3z = -2
2x-3y+5z = 1
4x+3y−4z = 9

Answer 1

To solve the given system of equations, you can use the elimination method. Multiply and add the equations to eliminate variables and then solve for the remaining variables. The solution to the system of equations is x = 1, y = 3, z = 0.

Step-by-step explanation:

To solve the given system of equations:

7x - 3y + 3z = -22

2x - 3y + 5z = 14

4x + 3y - 4z = 9

1. Choose a method to solve the system of equations. One method is elimination.
2. Multiply the first equation by 2 and the second equation by -7 to eliminate the y variable:
3. 14x - 6y + 6z = -44-14x + 21y - 35z = -98
4. Add the resulting equations:
5. 15y - 29z = -142
6. Multiply the second equation by 4 and the third equation by 2 to eliminate the y variable:
7. 8x - 12y + 20z = 568x + 6y - 8z = 18
8. Add the resulting equations:
9. 16x + 12z = 74
10. Multiply the third equation by 2 and the resulting equations by -15 to eliminate the x variable:
11. -14x + 21y - 35z = -210-16x - 12z = -1110
12. Add the resulting equations:
13. 21y - 47z = -1320
14. Now, you have a system of two equations with two variables:
15. 15y - 29z = -14221y - 47z = -1320
16. Using substitution or elimination, solve for y and z.
17. Once you have the values of y and z, substitute them back into any of the original equations to solve for x.

The solution to the system of equations is:

x = 1, y = 3, z = 0