Final answer:
To find the value of y in the system of equations x + y = b and −x + 3y = a, you substitute x from the first equation into the second and simplify, yielding y = (a + b) / 4.
Step-by-step explanation:
Steps to Solve for y
To solve the system of equations x + y = b and −x + 3y = a for y, we can use the method of elimination or substitution. Given that the question already provides a relationship for y in the form of y = 9 + 3x, it's implied that we should use this format as a guide.
First, from the equation x + y = b, express x in terms of y as x = b - y. Now, substitute this expression into the second equation:
−(b - y) + 3y = a, which simplifies to −b + y + 3y = a. Combine like terms to get 4y = a + b. Finally, divide by 4 to isolate y: y = (a + b) / 4.
Note that our solution does not match the initial reference to the equation y = 9 + 3x. This is because the equations we're solving are from the question and not related to the provided reference information.