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Julie and Bill are waiters at the Ogling Ogre Convention Center, which is well-known for serving the most deliciously disgusting meals to its guests. One of their tasks was to count the 2-eyed and 3-eyed ogres that arrived in order for the chef to know how many of each meal to plate.

When they reported their findings, Julie said, “I counted 12 heads.” Bill added, “I counted 28 eyes.” The chef was upset … “How many 2-eyed ogres were there? How many 3-eyed ogres were there?” he asked. “Unfortunately, there is no time to count again. You will have to figure out how many 2-eyed and 3-eyed ogres there are from that information. Let me know the answer immediately. You know how angry ogres get when they are hungry.” Can you help Julie and Bill figure out how many 2-eyed and 3-eyed ogres there are? Use matrices to solve the problem.

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Let $h_2$ be the number of two-eyed ogres and $h_3$ be the number of three-eyed ogres. The objective is to find $h_2$ and $h_3$.

There were $12$ heads in total, and $28$ eyes. We can express this using the following pair of equations:- $$h_2+h_3=12$$ $$2h_2+3h_3=28$$

In matrix format, this would be expressed as:-

$$\left( \begin{array}{cc} 1 & 1 \\ 2 & 3 \ \end{array} \right) \left( \begin{array}{cc} h_2 \\ h_3 \ \end{array} \right)=\left( \begin{array}{cc}12 \\ 28 \end{array} \right)$$ Can you take it from here?

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