Question:
Let $A \times B=\{(a, b): b=3 a-2\}$. if $(x,-5)$ and $(2, y)$ belong to $A \times B$, find the values of x and y.
Solution:
Given: $A \times B=\{(a, b): b=3 a-2\}$
and $\{(x,-5),(2, y)\} \in A \times B$
For $(x,-5) \in A \times B$
$b=3 a-2$
$\Rightarrow-5=3(x)-2$
$\Rightarrow-5+2=3 x$
$\Rightarrow-3=3 x$
$\Rightarrow x=-1$
For $(2, y) \in A \times B$
$b=3 a-2$
$\Rightarrow y=3(2)-2$
$\Rightarrow y=6-2$
$\Rightarrow y=4$
Hence, the value of x = -1 and y = 4
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