[tex] x + y = 30[/tex]
[tex] 5x + 10 y = 210 [/tex]
As a matrix equation that's
[tex] \begin{pmatrix} 1 & 1 \\ 5 & 10 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix}30\\ 210 \end{pmatrix}[/tex]
Answer:
The equation could be
[tex]\left[\begin{array}{ccc}1&1\\0.05&0.1\end{array}\right] \times \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}30\\2.10\end{array}\right][/tex]
Step-by-step explanation:
The equation to represent the number of coins would be
x + y = 30
The equation to represent the amount of money the coins are worth would be
0.05x + 0.10y = 2.10
This gives us the system
[tex]\left \{ {{x+y=30} \atop {0.05x+0.10y=2.10}} \right.[/tex]
Using matrices, the first matrix will be the coefficient matrix. Â This contains the coefficients for x and y for both equations:
[tex]\left[\begin{array}{ccc}1&1\\0.05&0.10\end{array}\right][/tex]
The second matrix will be the variable matrix, containing the variables for both equations:
[tex]\left[\begin{array}{ccc}x\\y\end{array}\right][/tex]
The matrix after the equals sign will be the constant matrix:
[tex]\left[\begin{array}{ccc}30\\2.10\end{array}\right][/tex]
This gives us the matrix equation above.
