Question

How can you represent the system of equations with a matrix?
[2x - 5y = 5
14x + 7y=-8

Answer 1

To represent the system of equations 2x - 5y = 51 and 4x + 7y = -8 as a matrix, we arrange the coefficients into the matrix A, variables into matrix x, and constants into matrix b, resulting in the matrix equation Ax = b.

Step-by-step explanation:

To represent a system of equations with a matrix, we first collect the coefficients of the variables and the constants from each equation. For the given system:

2x - 5y = 51
4x + 7y = -8

We can write this system as a matrix equation Ax = b, where A is the coefficient matrix, x is the variable matrix, and b is the constant matrix:

A = \begin{bmatrix} 2 & -5 \\ 4 & 7 \end{bmatrix},
x = \begin{bmatrix} x \\ y \end{bmatrix},
b = \begin{bmatrix} 51 \\ -8 \end{bmatrix}

So the matrix representation of the system is:

\begin{bmatrix} 2 & -5 \\ 4 & 7 \end{bmatrix} * \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 51 \\ -8 \end{bmatrix}