The graphs of `2x + 1 = 0` and `3y - 9 = 0` intersect at the point.
2x + 1 = 0 और 3y - 9 = 0 का आरेख (ग्राफ) किस बिन्दु पर प्रतिच्छेद करता है?

Options

A. `(-1/2 , 3)`
B. `(1/2, -3)`
C. `(-1/2 , -3)`
D. none of these

Explanation

To find the point of intersection of the graphs of the equations \(2x + 1 = 0\) and \(3y - 9 = 0\), we will solve each equation for \(x\) and \(y\) respectively.

### Step 1: Solve the first equation for \(x\)
The first equation is:
\[ 2x + 1 = 0 \]
To isolate \(x\), we will subtract 1 from both sides:
\[ 2x = -1 \]
Next, we divide both sides by 2:
\[ x = -\frac{1}{2} \]

### Step 2: Solve the second equation for \(y\)
The second equation is:
\[ 3y - 9 = 0 \]
To isolate \(y\), we will add 9 to both sides:
\[ 3y = 9 \]
Next, we divide both sides by 3:
\[ y = 3 \]

### Step 3: Write the point of intersection
Now that we have the values of \(x\) and \(y\), we can write the point of intersection:
\[ \text{Point of intersection} = \left(-\frac{1}{2}, 3\right) \]

### Final Answer
The graphs of \(2x + 1 = 0\) and \(3y - 9 = 0\) intersect at the point \(\left(-\frac{1}{2}, 3\right)\).

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