If `10a=6b+7 and a-6b=34`, then what is the value of `(-1)/(3)a`?

Options

A. `-1`
B. `1`
C. `(41)/(27)`
D. `(41)/(9)`

Explanation

To solve the system of equations given by \(10a = 6b + 7\) and \(a - 6b = 34\), we will follow these steps:

### Step 1: Rewrite the equations in standard form
We can rewrite the first equation \(10a = 6b + 7\) in the standard form \(Ax + By = C\):
\[ 10a - 6b = 7 \]
The second equation \(a - 6b = 34\) is already in standard form:
\[ a - 6b = 34 \]

### Step 2: Set up the system of equations
Now we have the following system of equations:
1. \(10a - 6b = 7\) (Equation 1)
2. \(a - 6b = 34\) (Equation 2)

### Step 3: Eliminate \(b\)
To eliminate \(b\), we can subtract Equation 2 from Equation 1. First, we need to express both equations in a way that allows us to eliminate \(b\):
\[ 10a - 6b - (a - 6b) = 7 - 34 \]
This simplifies to:
\[ 10a - 6b - a + 6b = 7 - 34 \]
\[ 9a = -27 \]

### Step 4: Solve for \(a\)
Now we can solve for \(a\):
\[ a = \frac{-27}{9} = -3 \]

### Step 5: Find the value of \(-\frac{1}{3}a\)
Now that we have the value of \(a\), we can find \(-\frac{1}{3}a\):
\[ -\frac{1}{3}a = -\frac{1}{3} \times (-3) = 1 \]

### Final Answer
The value of \(-\frac{1}{3}a\) is \(1\).

---