Final answer:
To solve the given system of linear equations, algebraic methods such as elimination can be used to find the values of x, y, and z that satisfy all three equations.
Step-by-step explanation:
The question involves solving a system of linear equations using algebraic methods such as substitution, elimination, or matrix operations. The system provided is:
- A) x + y + 3z = 12
- B) -3x + 7y - 2z = -35
- C) 7x - 6y - 5z = 32
To solve the system, we can use the elimination method to eliminate one variable and solve for the other two, and then back-substitute to find the third variable. This process may require multiple steps and careful checking of your work as you solve. Once solved, the solution will provide values for x, y, and z that satisfy all three equations simultaneously.
Simplifying the equation, we get: -8z = -40
Finally, substitute the value of z into the equation we obtained earlier to solve for y:
9y + 9(-5) = 21
Simplifying the equation, we get: 9y = 66
From there, we can solve for y, substitute the values of y and z into one of the original equations to solve for x.