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Question

# Write the system of equations represented by the matrix equation below. Then solve matrix equation.$\left[ \begin{array} { r r } { - 3 } & { - 2 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l } { x } \\ { y } \end{array} \right] = \left[ \begin{array} { r } { 1 } \\ { - 3 } \end{array} \right]$

Solution

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Step 1
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The given matrix equation is in the form:

$AX=B$

where $A$ is the coefficient matrix, $X$ is the variable matrix, and $B$ is the constant matrix.

By multiplying $A$ and $X$ we have:

$AX= \left[\begin{array}{rr} -3(x)+(-2)(y) \\ 5(x)+4(y) \end{array}\right]= \left[\begin{array}{rr} -3x-2y\\ 5x+4y \end{array}\right]$

So, the system of equations is:

$\color{#c34632}{\begin{cases} -3x-2y=1\\ 5x+4y=-3 \end{cases}}\color{white}{\tag{1}}$

The solution of the system is:

$X=A^{-1}B$

Using a graphing calculator, we input the coefficient matrix on [A] and the constant matrix on [B]:

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