Question

Which matrix equation can be used to solve the systems of equations below?

Answer 1

Answer:

The matrix equation that can be used to solve the system is  $\[\begin{bmatrix}3 & -2\\6&-5\\\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-3\\-9\end{bmatrix}\]$

Step-by-step explanation:

A matrix is an array of numbers.

A matrix equation is an equation of the form  $Ax=b$ where $A$ is coefficient matrix, $x$ is the variable matrix,  and $b$ is the constant matrix.

To express this system

                                                $\begin{cases}3x - 2y = -3\\6x - 5y = -9\end{cases}$

in matrix form, you follow three simple steps:

1. Write all the coefficients in one matrix first.
2. Multiply this matrix with the variables of the system set up in another matrix.
3. Insert the answers on the other side of the equal sign in another matrix.

Therefore, the matrix equation that can be used to solve the system is

                                              $\[\begin{bmatrix}3 & -2\\6&-5\\\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-3\\-9\end{bmatrix}\]$