If the point (2,3) lies on the graph of the equation ax+2y =10, find the value of a

Answer

To find the value of \( a \) in the equation \( ax + 2y = 10 \) given that the point \( (2, 3) \) lies on its graph, we can follow these steps:

### Step 1: Substitute the coordinates into the equation
Since the point \( (2, 3) \) lies on the graph, we can substitute \( x = 2 \) and \( y = 3 \) into the equation \( ax + 2y = 10 \).

\[ a(2) + 2(3) = 10 \]

### Step 2: Simplify the equation
Now, simplify the left-hand side of the equation:

\[ 2a + 6 = 10 \]

### Step 3: Isolate the term with \( a \)
Next, we need to isolate the term with \( a \) by subtracting 6 from both sides:

\[ 2a = 10 - 6 \]

\[ 2a = 4 \]

### Step 4: Solve for \( a \)
Now, divide both sides by 2 to solve for \( a \):

\[ a = \frac{4}{2} \]

\[ a = 2 \]

### Final Answer
Thus, the value of \( a \) is \( 2 \).

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