I need some help with this system, please!

Question

 

2f(x-1) + g(x+1) = 7x - 4

3f(x-1) - 4g(x+1)= -6x-39

Answer 1

This is not different from solving for more that two variables.  Only this time, you are solving for functions.

 

 

Multiply the first equation by 4 and keep the second equation.

 

8f(x - 1) + 4g(x + 1) = 28x - 16

3f(x - 1) - 4g(x + 1) = -6x - 39

 

Add the equations.

 

11f(x - 1) = 22x - 56

 

 

Divide both sides of the equation by 11.

 

f(x - 1) = (22x - 56) / 11

 

 

Substitute this value of f(x - 1) into the second equation to solve for g(x + 1).