Question

Represent the system of equations in augmented matrix form.
y =1/4x–3 y=–3x+5

Answer 1

`\left[\begin{array}cc1&-4&12\\3&1&5\end{array}\right]`

Explanation:

You want these equations represented as an augmented matrix.

• y = 1/4x -3
• y = -3x +y

Augmented matrix

An augmented matrix of the coefficients of a system of equations is a representation of that system when it is written in standard form. We can convert these equations to standard form to facilitate writing the matrix.

y = 1/4x -3

4y = x -12 . . . . . multiply by 4

x -4y = 12 . . . . . add 12 -4y

and

y = -3x +5

3x +y = 5 . . . . . add 3x

The matrix representing these two equations looks like ...

`\boxed{\left[\begin{array}c1&-4&12\\3&1&5\end{array}\right] }`

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Additional comment

The solution is shown in the attachment. It is found by reducing the augmented matrix to row-echelon form with the left side being the identity matrix.

(x, y) = (32/13, -31/13)

<95141404393>