represent the system of equations in augmented matrix form

y= 1/4x -3
y=-3x +5

Rewrite things as

x-4y=12
3x+y=5
and the matrix is
(1 -4 | 12)
(3 1 | 5)

To represent the system of equations in augmented matrix form, we can write the coefficients of the variables followed by the constants on the right side of the equation.

The given equations are:
1) y = (1/4)x - 3
2) y = -3x + 5

We'll rearrange these equations in a standard form with all terms on one side:
1) (1/4)x - y = -3
2) 3x + y = 5

Now, we can write the coefficients of x, y, and the constants in an augmented matrix as follows:

[1/4 -1 -3]
[3 1 5]

To represent a system of equations in augmented matrix form, we need to arrange the coefficients of the variables and constants into a matrix.

Let's start by writing the equations in standard form:
1) y = (1/4)x - 3
2) y = -3x + 5

Now, we can rewrite these equations in the form ax + by = c. Rearrange the equations to have the variables on the left side and constants on the right side:
1) (1/4)x - y = -3
2) 3x + y = 5

Now, we can write the coefficients of x, y, and the constants into an augmented matrix.

The augmented matrix [A|B] is formed by taking the coefficients of x and y and the constant term, and arranging them row by row:

| 1/4 -1 -3 |
[A|B]=| 3 1 5 |

So, the augmented matrix representation of the given system of equations is:

| 1/4 -1 -3 |
[A|B]=| 3 1 5 |