If `-7` is one solution of the equation `y^(2)+cy-35=0`, what is the value of c?

Explanation

To find the value of \( c \) in the equation \( y^2 + cy - 35 = 0 \) given that one solution is \( -7 \), we can follow these steps:

### Step 1: Substitute the solution into the equation
Since \( -7 \) is a solution, we substitute \( y = -7 \) into the equation:
\[ (-7)^2 + c(-7) - 35 = 0 \]

### Step 2: Simplify the equation
Calculating \( (-7)^2 \) gives us \( 49 \). Thus, we rewrite the equation:
\[ 49 + c(-7) - 35 = 0 \]

### Step 3: Combine like terms
Now, simplify the equation:
\[ 49 - 35 - 7c = 0 \]
This simplifies to:
\[ 14 - 7c = 0 \]

### Step 4: Solve for \( c \)
To isolate \( c \), we can rearrange the equation:
\[ -7c = -14 \]
Dividing both sides by \( -7 \) gives:
\[ c = 2 \]

### Final Answer
The value of \( c \) is \( 2 \).

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