No.126 Parameters in a System
Example
The solution of the system \(\begin{cases}2ax-y=11\\ax+3by=12\end{cases}\) is \(x=2,\ y=1\). Find the values of \(a\) and \(b\).
POINT
Substitute the given solution into both equations to find the unknown coefficients.
\(a=3,\ b=2\)
TRY
TRY 1
The solution of \(\begin{cases}ax+y=7\\2x+by=8\end{cases}\) is \(x=2,\ y=1\). Find \(a\) and \(b\).
\(a=3,\ b=4\)
TRY 2
The solution of \(\begin{cases}2ax+y=15\\x+by=8\end{cases}\) is \(x=2,\ y=3\). Find \(a\) and \(b\).
\(a=3,\ b=2\)