Simultaneous Equations

A student solves:
\begin{aligned}
2x+3y&=13 &&(1)\\
4x-y&=5 &&(2)
\end{aligned}
Their working is:
\begin{aligned}
(1)\times2:\quad 4x+6y&=26\\
(4x+6y)-(4x-y)&=26-5\\
5y&=21\\
y&=\frac{21}{5}.
\end{aligned}

1. Identify the first incorrect step and explain it.

2. Find the correct values of \(x\) and \(y\).

3. A student later rounds an incorrect answer to \(x=2.3,\ y=4.2\). Test this pair in the original equations and explain why checking both equations matters.