Question

If the ordered pairs \((2x-3,-5)\) and \((x,y-1)\) are equal, then find the value of \(x\) and \(y\).

Hint:

Equal ordered pairs mean the first entries are equal and the second entries are equal.

Answer 1

Step 1: Treat this as two separate one-variable equations:
Since ordered pairs match position by position, the first entries give $2x-3=x$ and the second entries give $-5=y-1$; there is no mixing between the two.

Step 2: Solve the x-equation:
$2x-3=x \Rightarrow 2x-x=3 \Rightarrow x=3$.

Step 3: Solve the y-equation:
$-5=y-1 \Rightarrow y=-5+1=-4$.

Final Answer:
$x=3$, $y=-4$. \[ \boxed{x=3,\ y=-4} \]