If `2x + y = 6 and x = 2` are two linear equations, then graph of two equations meet at a point

Options

A. `(0,2)`
B. `(2,2)`
C. `(1,2)`
D. `(2,0)`

Answer

To find the point where the graphs of the two equations \(2x + y = 6\) and \(x = 2\) meet, we can follow these steps:

### Step 1: Write down the equations
We have the following two equations:
1. \(2x + y = 6\)
2. \(x = 2\)

### Step 2: Substitute the value of \(x\) into the first equation
Since we know \(x = 2\), we can substitute this value into the first equation:
\[ 2(2) + y = 6 \]

### Step 3: Simplify the equation
Now, calculate \(2(2)\):
\[ 4 + y = 6 \]

### Step 4: Solve for \(y\)
To find \(y\), subtract 4 from both sides:
\[ y = 6 - 4 \]
\[ y = 2 \]

### Step 5: Write the solution as a point
Now we have both \(x\) and \(y\):
\[ (x, y) = (2, 2) \]

Thus, the point where the graphs of the two equations meet is \((2, 2)\).

### Conclusion
The correct option is the second one: \((2, 2)\).

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