`x+7y=-10`
`3x-4y=k`
In the system of equation above,k is a constant. IF (a,b) is the solution to the system, what is the value of a, in terms of k?

Options

A. `(-k-30)/25`
B. `(3k+10)/25`
C. `(6k-8)/25`
D. `(7k-40)/25`

Answer

To solve the system of equations given by:

1. \( x + 7y = -10 \) (Equation 1)
2. \( 3x - 4y = k \) (Equation 2)

We need to find the value of \( a \) (which represents \( x \)) in terms of \( k \).

### Step 1: Multiply the equations to eliminate \( y \)

We will first eliminate \( y \) by making the coefficients of \( y \) in both equations equal. We can do this by multiplying Equation 1 by 4 and Equation 2 by 7.

- Multiply Equation 1 by 4:
\[ 4(x + 7y) = 4(-10) \implies 4x + 28y = -40 \quad \text{(Equation 3)} \]

- Multiply Equation 2 by 7:
\[ 7(3x - 4y) = 7k \implies 21x - 28y = 7k \quad \text{(Equation 4)} \]

### Step 2: Add the two new equations

Now we will add Equation 3 and Equation 4 to eliminate \( y \):

\[ (4x + 28y) + (21x - 28y) = -40 + 7k \]

This simplifies to:
\[ 25x = 7k - 40 \]

### Step 3: Solve for \( x \)

Now, we can solve for \( x \) (which is \( a \)):
\[ x = \frac{7k - 40}{25} \]

Thus, the value of \( a \) in terms of \( k \) is:
\[ a = \frac{7k - 40}{25} \]

### Final Answer
The value of \( a \) in terms of \( k \) is:
\[ \boxed{\frac{7k - 40}{25}} \]