`x+y=29`
`x+2y=12`
If the ordered pair (x, y) is the solution to the system of equations above, what is the value of y?

Options

A. `-17`
B. `12`
C. `46`
D. `75`

Explanation

To solve the system of equations given by:

1. \( x + y = 29 \) (Equation 1)
2. \( x + 2y = 12 \) (Equation 2)

we will use the elimination method to find the value of \( y \).

### Step 1: Rearrange the equations
We can express \( x \) from Equation 1:

\[ x = 29 - y \]

### Step 2: Substitute \( x \) in Equation 2
Now, we will substitute \( x \) in Equation 2:

\[ (29 - y) + 2y = 12 \]

### Step 3: Simplify the equation
Now, simplify the equation:

\[ 29 - y + 2y = 12 \]

Combine like terms:

\[ 29 + y = 12 \]

### Step 4: Isolate \( y \)
Now, isolate \( y \) by subtracting 29 from both sides:

\[ y = 12 - 29 \]

\[ y = -17 \]

### Conclusion
The value of \( y \) is \( -17 \).

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