#### Answer

$r=5 \% $ and $Y=1200$

#### Work Step by Step

We need to solve the given system of equations as follows: $$0.05Y−1000r=10~~~~(1) \\ 0.05Y+800r=100~~~~(2)$$
We will multiply equation $(1)$ by $-1$.
$$-0.05Y+1000r=-10~~~~(3)$$
Add equations $(2)$ and $(3)$ to eliminate Y.
$$0.05Y+800r-0.05Y+1000r =100-10 \\ 1800 r =90 \\ r=0.05= 5 \%$$
Now, back substitute the value of $r$ into Equation $(1)$ to solve for $Y$:
$$0.05Y−1000(0.05)=10 \\ 0.05Y -50=10 \\ Y=1200$$
Therefore, our results are: $r=5 \% $ and $Y=1200$