Certainly! Let's break down the problem step-by-step to find three different pairs of values for [tex]\(a\)[/tex] and [tex]\(b\)[/tex] that satisfy the equation:
[tex]\[
19 = a \cdot b + 7
\][/tex]
First, we should rearrange the equation to make it easier to find pairs [tex]\((a, b)\)[/tex]:
[tex]\[
19 - 7 = a \cdot b \implies 12 = a \cdot b
\][/tex]
Now, we need to find pairs of whole numbers [tex]\((a, b)\)[/tex] such that their product is 12. Let's list the factor pairs of 12:
The factor pairs of 12 are:
1. [tex]\((1, 12)\)[/tex]
2. [tex]\((2, 6)\)[/tex]
3. [tex]\((3, 4)\)[/tex]
4. [tex]\((4, 3)\)[/tex]
5. [tex]\((6, 2)\)[/tex]
6. [tex]\((12, 1)\)[/tex]
From these pairs, we can select three different pairs where [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are whole numbers:
[tex]\[
\begin{array}{|l|l|}
\hline
\text{Value of } a & \text{Value of } b \\
\hline
1 & 12 \\
\hline
2 & 6 \\
\hline
3 & 4 \\
\hline
\end{array}
\][/tex]
Thus, the three different possible pairs of values for [tex]\(a\)[/tex] and [tex]\(b\)[/tex] that satisfy the equation [tex]\(19 = a \cdot b + 7\)[/tex] are:
[tex]\[
(1, 12), (2, 6), (3, 4)
\][/tex]
