If the Ordered Pairs \( (x,-1) \) and \( (5,y) \) Belong to the Set \( \{(a,b): b=2a-3\} \), Find \(x\) and \(y\)
Question
If the ordered pairs \[ (x,-1) \] and \[ (5,y) \] belong to the set \[ \{(a,b): b=2a-3\}, \] find the values of \(x\) and \(y\).
Solution
Given relation:
\[ b=2a-3 \]
For the ordered pair \((x,-1)\),
\[ a=x,\quad b=-1 \]
Substituting in the relation:
\[ -1=2x-3 \]
\[ 2x=-1+3 \]
\[ 2x=2 \]
\[ x=1 \]
Now for the ordered pair \((5,y)\),
\[ a=5,\quad b=y \]
Substituting in the relation:
\[ y=2(5)-3 \]
\[ y=10-3 \]
\[ y=7 \]
Therefore,
\[ \boxed{x=1,\ y=7} \]