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 lines represented by the equations \(6x - 3y + 10 = 0\) and \(2x - y + 9 = 0\), we will analyze the equations step by step.

### Step 1: Rewrite the equations in slope-intercept form
We start by rewriting both equations in the slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

1. **For the first equation:**
\[ 6x - 3y + 10 = 0 \]
Rearranging gives:
\[ -3y = -6x - 10 \implies y = 2x + \frac{10}{3} \]
Here, the slope \(m_1 = 2\).

2. **For the second equation:**
\[ 2x - y + 9 = 0 \]
Rearranging gives:
\[ -y = -2x - 9 \implies y = 2x + 9 \]
Here, the slope \(m_2 = 2\).

### Step 2: Compare the slopes
Now that we have both equations in slope-intercept form, we can compare their slopes:
- The slope of the first line \(m_1 = 2\).
- The slope of the second line \(m_2 = 2\).

Since both slopes are equal (\(m_1 = m_2\)), the lines are either parallel or coincident.

### Step 3: Check for y-intercepts
Next, we check the y-intercepts to determine if the lines are coincident or parallel:
- The y-intercept of the first line is \(\frac{10}{3}\).
- The y-intercept of the second line is \(9\).

Since the y-intercepts are different, the lines are not coincident.

### Conclusion
Since both lines have the same slope but different y-intercepts, we conclude that the lines represented by the equations \(6x - 3y + 10 = 0\) and \(2x - y + 9 = 0\) are parallel lines.

### Final Answer
Therefore, the pair of lines given above are parallel lines.

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