Final answer:
After solving the given system of equations, the value of y is determined to be 6.4, but this answer does not match any of the provided choices. There appears to be an error in the options given or the original equations.
Step-by-step explanation:
To find the value of y in the solution to the system of equations, we first need to solve the system. We have two equations:
x + y = 1
2x – 3y = –30
From the first equation, we can express x in terms of y:
x = 1 - y
Next, we substitute this expression for x into the second equation:
2(1 - y) - 3y = -30
Expanding this equation:
2 - 2y - 3y = -30
Combining like terms:
-5y = -32
Divide both sides by -5 to find the value of y:
y = 32 / 5
Now, we can see that none of the options provided in the question (-8, -3, 3, 8) match the correct value we found, which is 6.4. It seems there might be an error in the options provided. However, if the question intended for y to be an integer, then we should re-examine the arithmetic or consider that there might be a typo in the original equations or options given.