3. The constant of proportionality between the number of cats (c) in a pet shelter and the number of dogs (d) in the shelter is
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The matrix represents the system:
-3x+5y=15
2x+3y=-10, which is choice c.
We can see it more clearly from the way we multiply matrices, as follows:
![\[ \left[ {\begin{array}{cc} -3 & 5 \\ \ 2 & 3 \\ \end{array} } \right] \] \cdot \[ \left[ {\begin{array}{c} x \\ y \\ \end{array} } \right] \]= \left[ {\begin{array}{c} -3\cdot x+5\cdot y \\ 2\cdot x+3\cdot y \\ \end{array} } \right] \]= \[ \left[ {\begin{array}{c} 15 \\ -10 \\ \end{array} } \right] \]](https://tex.z-dn.net/?f=%20%5C%5B%0A%20%20%5Cleft%5B%20%7B%5Cbegin%7Barray%7D%7Bcc%7D%0A%20%20%20-3%20%26%205%20%5C%5C%0A%20%20%20%20%5C%202%20%20%26%203%20%5C%5C%0A%20%20%5Cend%7Barray%7D%20%7D%20%5Cright%5D%0A%5C%5D%20%5Ccdot%20%20%5C%5B%0A%20%20%5Cleft%5B%20%7B%5Cbegin%7Barray%7D%7Bc%7D%0A%20%20%20x%20%5C%5C%0A%20%20%20%20y%20%5C%5C%0A%20%20%5Cend%7Barray%7D%20%7D%20%5Cright%5D%0A%5C%5D%3D%20%5Cleft%5B%20%7B%5Cbegin%7Barray%7D%7Bc%7D%0A%20%20%20-3%5Ccdot%20x%2B5%5Ccdot%20y%20%5C%5C%0A%20%20%20%202%5Ccdot%20x%2B3%5Ccdot%20y%20%5C%5C%0A%20%20%5Cend%7Barray%7D%20%7D%20%5Cright%5D%0A%5C%5D%3D%20%5C%5B%20%5Cleft%5B%20%7B%5Cbegin%7Barray%7D%7Bc%7D%2015%20%5C%5C%20-10%20%5C%5C%20%5Cend%7Barray%7D%20%7D%20%5Cright%5D%20%5C%5D)
Answer: C
-3x+5y=15
2x+3y=-10, which is choice c.
We can see it more clearly from the way we multiply matrices, as follows:
Answer: C