Questions: For what value of k will the relation S=(2k+3,1),(3k-1,-2) not be a function?

For what value of k will the relation S=(2k+3,1),(3k-1,-2) not be a function?
Transcript text: 15 For what value of $k$ will the relation $S=\{(2 k+3,1),(3 k-1,-2)\}$ not be a function?
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Solution

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Solution Steps

To determine the value of \( k \) for which the relation \( S = \{(2k+3, 1), (3k-1, -2)\} \) is not a function, we need to find when the x-values (first elements of the ordered pairs) are the same. This is because a relation is not a function if any x-value maps to more than one y-value. Therefore, we set \( 2k + 3 \) equal to \( 3k - 1 \) and solve for \( k \).

Step 1: Set Up the Equation

To determine the value of \( k \) for which the relation \( S = \{(2k+3, 1), (3k-1, -2)\} \) is not a function, we need to find when the x-values (first elements of the ordered pairs) are the same. This is because a relation is not a function if any x-value maps to more than one y-value. Therefore, we set \( 2k + 3 \) equal to \( 3k - 1 \).

Step 2: Solve the Equation

We solve the equation \( 2k + 3 = 3k - 1 \) for \( k \).

\[ 2k + 3 = 3k - 1 \]

Subtract \( 2k \) from both sides:

\[ 3 = k - 1 \]

Add 1 to both sides:

\[ k = 4 \]

Final Answer

The value of \( k \) for which the relation \( S = \{(2k+3, 1), (3k-1, -2)\} \) is not a function is \( \boxed{4} \).

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