No.127 Two Systems with the Same Solution
Example
\(\begin{cases}x+y=5\\x-y=-1\end{cases}\qquad\begin{cases}ax+y=7\\x+by=8\end{cases}\quad a=?,\ b=?\)
POINT
Solve the first system for x and y, then substitute into the second to find a and b.
\(x=2,\ y=3,\ a=2,\ b=2\)
TRY
TRY 1
\(\begin{cases}x+y=4\\x-y=2\end{cases}\qquad\begin{cases}ax+y=10\\x+by=5\end{cases}\quad a=?,\ b=?\)
\(x=3,\ y=1,\ a=3,\ b=2\)
TRY 2
\(\begin{cases}x+y=5\\x-y=-3\end{cases}\qquad\begin{cases}ax+y=6\\x+by=13\end{cases}\quad a=?,\ b=?\)
\(x=1,\ y=4,\ a=2,\ b=3\)
TRY 3
\(\begin{cases}x+y=2\\x-y=-4\end{cases}\qquad\begin{cases}ax+y=1\\x+by=-7\end{cases}\quad a=?,\ b=?\)
\(x=-1,\ y=3,\ a=2,\ b=-2\)
TRY 4
\(\begin{cases}x+y=2\\x-y=6\end{cases}\qquad\begin{cases}ax+y=10\\x+by=0\end{cases}\quad a=?,\ b=?\)
\(x=4,\ y=-2,\ a=3,\ b=2\)
TRY 5
\(\begin{cases}x+y=-5\\x-y=1\end{cases}\qquad\begin{cases}ax+y=1\\x+by=-11\end{cases}\quad a=?,\ b=?\)
\(x=-2,\ y=-3,\ a=-2,\ b=3\)