Graphically, the pair of equations
`6x - 3y+10 = 0`
`2x - y + 9 = 0`
represents two lines which are

Options

A. intersecting at exactly one point
B. intersecting exactly two points
C. coincident
D. parallel

Explanation

To determine the relationship between the two equations graphically, we will analyze the equations step by step and plot them on a graph.

### Step 1: Write down the equations
The given equations are:
1. \( 6x - 3y + 10 = 0 \)
2. \( 2x - y + 9 = 0 \)

### Step 2: Rearrange each equation into slope-intercept form
We will rearrange both equations into the form \( y = mx + b \) where \( m \) is the slope and \( b \) is the y-intercept.

**For the first equation:**
\[ 6x - 3y + 10 = 0 \implies -3y = -6x - 10 \implies y = 2x + \frac{10}{3} \]

**For the second equation:**
\[ 2x - y + 9 = 0 \implies -y = -2x - 9 \implies y = 2x + 9 \]

### Step 3: Identify the slopes and y-intercepts
From the rearranged equations:
- The first equation \( y = 2x + \frac{10}{3} \) has a slope \( m_1 = 2 \) and y-intercept \( b_1 = \frac{10}{3} \).
- The second equation \( y = 2x + 9 \) has a slope \( m_2 = 2 \) and y-intercept \( b_2 = 9 \).

### Step 4: Compare the slopes
Since both equations have the same slope \( m_1 = m_2 = 2 \), the lines represented by these equations are parallel.

### Step 5: Check for intersection
Parallel lines do not intersect, which means there is no solution to the system of equations.

### Conclusion
The pair of equations \( 6x - 3y + 10 = 0 \) and \( 2x - y + 9 = 0 \) represent two parallel lines.

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