Answer
$r=0.06= 6 \% $ and $Y=9000$
Work Step by Step
We need to solve the system of equations as follows: $$0.06Y−5000r=240~~~~(1) \\ 0.06Y+6000r=900~~~~(2)$$
We will multiply equation (1) by $-1$.
$$-0.06Y+5000r=-240~~~~(3)$$
Now, add equations (2) and (3) to eliminate $Y$.
$$0.06Y+6000r−0.06Y+5000r=900−240~~~~(4)\\ 11000 r =660 \\ r=0.06= 6 \%$$
Now, back substitute the value of $r$ into Equation (1) to solve for $Y$:
$$0.06Y-5000 (0.06)=240 \\ 0.06Y =240+300 \\ 0.06 Y =540 \\ Y=\dfrac{540}{0.06} \\ Y=9000$$
Therefore, our results are: $r=0.06= 6 \% $ and $Y=9000$
