Answer
a) $x=90000$ and $y=60000$
b) $x=130000$ and $y=20000$
Work Step by Step
a) Let $x$ be the amount to be invested in AA bonds yielding $10\%$ and $y$ be the amount to be invested in Bank Certificate yielding $5\%$.
$\begin{cases}0.1x+0.05y=12000\\
x+y=150000,
\end{cases}$
Multiplying the second equation by $-0.05$ and adding it to the first equation.
$\begin{cases}
0.1x+0.05y=12000\\
-0.05x-0.05y=-7500,\\
-- -- -- -- --\\
0.05x=4500,
\end{cases}$
Thus, $0.05x=4500, x=90000$ and $y=60000$
b) $\begin{cases}0.1x+0.05y=14000\\
x+y=150000,
\end{cases}$
Multiplying the second equation by $-0.05$ and adding it to the first equation.
$\begin{cases}
0.1x+0.05y=14000\\
-0.05x-0.05y=-7500,\\
-- -- -- -- --\\
0.05x=6500,
\end{cases}$
Thus, $0.05x=6500, x=130000$ and $y=20000$
