Question

Which is an augmented matrix for the system of linear equations below?

-4x + 3y = 216
10x - 4y = -156

A. [4 3]
[10 4]

B. [-4 3]
[10 -4]

C. [ 4 3 216]
[10 4 156]

D. [-4 3 216]
[10 -4 -156]

Answer 1

`\left\{\begin{array}{ccc}-4x+3y=216\\10x-4y=-156\end{array}\right\\\\Answer:\\D.\ \left[\begin{array}{ccc}-4&3&216\\10&-4&-156\end{array}\right]`
the first column is the number next to x
the second column is the number next to y
the third column is the number without the x and y sign to the right of the equal sign

Answer 2

Option D is right

Explanation:

Given is a system of linear equations as

-4x+3y=216

10x-4y=-156

This is of the form

Ax=B

where A is the matrix formed by the coefficients of the variables and B is the constant on right side

Augmented matrix is the matrix where matrix A and B are written side by side

Here

A=
`\left[\begin{array}{ccc}-4&3&216\\10&-4&-156\end{array}\right]`