The lines `3x-4y=9 and y=0` meet at :

Options

A. `(-3,0)`
B. `(3,0)`
C. `9/4,0`
D. `(3/2,0)`

Answer

To find the point where the lines \(3x - 4y = 9\) and \(y = 0\) meet, we can follow these steps:

### Step 1: Substitute \(y = 0\) into the first equation
We start with the equation of the first line:
\[ 3x - 4y = 9 \]
Since we know that \(y = 0\), we substitute \(0\) for \(y\):
\[ 3x - 4(0) = 9 \]

### Step 2: Simplify the equation
This simplifies to:
\[ 3x = 9 \]

### Step 3: Solve for \(x\)
Now, we can solve for \(x\) by dividing both sides by \(3\):
\[ x = \frac{9}{3} = 3 \]

### Step 4: Write the coordinates of the intersection point
Now that we have both \(x\) and \(y\), we can write the coordinates of the point where the two lines meet:
\[ (x, y) = (3, 0) \]

### Final Answer
The lines \(3x - 4y = 9\) and \(y = 0\) meet at the point \((3, 0)\).

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