If \( (x+1,\ 1) = (3,\ y-2) \), Find the Values of \(x\) and \(y\)
Question
If \[ (x+1,\ 1)=(3,\ y-2) \] find the values of \(x\) and \(y\).
Solution
Since two ordered pairs are equal, their corresponding components are equal.
\[ x+1=3 \]
\[ x=3-1 \]
\[ x=2 \]
Now,
\[ 1=y-2 \]
\[ y=1+2 \]
\[ y=3 \]
Therefore, \[ \boxed{x=2,\ y=3} \]