which matrix represents the system of equations below.
-2x-7y=3
7x-6y=12
not sure how to figure this out.
To determine which matrix represents the given system of equations, we need to arrange the coefficients of the variables (x and y) in matrix form. The variables should be ordered in the same way in all equations.
First, let's rearrange the equations in standard form:
Equation 1: -2x - 7y = 3
Equation 2: 7x - 6y = 12
Now, we can write the coefficients of x and y as a matrix:
[ -2 -7 ] [ x ] = [ 3 ]
[ 7 -6 ] [ y ] [ 12 ]
Thus, the matrix representation of the given system of equations is:
[ -2 -7 ]
[ 7 -6 ]
The column on the right represents the constants on the other side of the equations, and the variables x and y are represented as a column matrix.
To find the matrix that represents the given system of equations, we need to arrange the coefficients of the variables in a matrix format.
Let's start by writing the coefficients of the variables x and y and the constant terms separately.
The given system of equations is:
-2x - 7y = 3 -- Equation (1)
7x - 6y = 12 -- Equation (2)
Writing the coefficients and constants in matrix form:
| -2 -7 | | x | = | 3 |
| 7 -6 | | y | | 12 |
Therefore, the matrix representation of the system of equations is:
|-2 -7|
| 7 -6|
This is the coefficient matrix on the left side of the equation, and the right side constants are placed in a separate column matrix on the right side.