x = cereal
y = milk
then, we have the expressions
2x + y = 340 and 3x + 2y = 570
solve for x and y:
[tex]\begin{gathered} \begin{bmatrix}2x+y=340 \\ 3x+2y=570\end{bmatrix} \\ x=\frac{340-y}{2} \\ 3\cdot\frac{340-y}{2}+2y=570 \\ \frac{1020+y}{2}=570 \\ \frac{2\left(1020+y\right)}{2}=570\cdot\: 2 \\ 1020+y=1140 \\ 1020+y-1020=1140-1020 \\ y=120 \end{gathered}[/tex]for x:
[tex]\begin{gathered} x=\frac{340-120}{2} \\ x=\frac{220}{2} \\ x=110 \end{gathered}[/tex]answer: 110 calories are in one cup of just cereal
