Answer
A meal contains $\dfrac{1}{3}$ cup of rice and $\dfrac{1}{5}$ cup of soybeans.
Work Step by Step
Let us suppose that $x$ and $y$ be the number of cups of protein (rice) and calories (soybeans) in a meal.
Thus, we can write the system of equations as:
$15x+22.5 y=9.5~~~(1) \\ 810 x+270 y=324 ~~~(2)$
Our aim is to multiply Equation (1) by $-4$ and then add to the equation -(2).
So, we have: $y=\dfrac{1}{5}$
Plug $y=\dfrac{1}{5}$ in equation (1) to obtain:
$15x+22.5 (1/5)=9.5 \implies x=\dfrac{1}{3}$
Therefore, a meal contains $\dfrac{1}{3}$ cup of rice and $\dfrac{1}{5}$ cup of soybeans.
