Final answer:
In the system of linear equations provided, the valid substitution is C) x = 15 - 3y, which is derived from the second equation by adding 3y to both sides and dividing by 6.
Step-by-step explanation:
In solving the system of linear equations given:
The valid substitutions that we can make to solve the equations involve isolating one variable in terms of the other. Given the options:
- A) Y = 15 - x/3
- B) y = -45 - x
- C) x = 15 - 3y
- D) X = 15 + 3y
Option A is not correct because it does not directly result from either of the original equations. Option B is not correct because it does not relate to the coefficients present in the original equations. Option C is a valid substitution derived from the second equation by adding 3y to both sides and dividing by 6.
Therefore:
6x - 3y = 15
Add 3y to both sides:
6x = 3y + 15
Divide by 6:
x = 15/6 + 3y/6
x = 2.5 + 0.5y
We can see that if we multiply both sides by 2, we get:
x = 5 + y
Which is closer to option C (after rearranging), making C the correct substitution.
Option D is not derived from the equations as provided. We need to focus on substitutions that closely follow from the original equations, keeping in mind the proper arithmetic operations to isolate the variables.