Question

What linear system of equations does the matrix represent?

[-3 5 | 15]
[2 3 | -10]
A. -3x=2
5x=3
15x=-10
B. -3y=2
5y=3
15y=-10
C. -3x+5y=15
2x+3y=-10
D. -3x+5y=-10
2x+3y=15

Answer 1

We read the equations one row at a time:

-3x + 5y = 15

2x + 3y = -10

Answer: C

Answer 2

Answer: C.

`-3x+5y=15\\\\2x+3y=-10`

Explanation:

Consider an Augmented matrix

`\begin{bmatrix} \left.\begin{matrix}a_(11) & a_(12) & \\ a_(21) & a_(22) & \end{matrix}\right|\left.\begin{matrix}b_(1) & \\ b_(2) & \end{matrix}\end{bmatrix}`

The linear system for above augmented matrix is given by :-

`a_(11)x+a_(12)y=b_1\\ a_(21)x+a_(22)y=b_(2)`

We are given an Augmented matrix as:

`\begin{bmatrix} \left.\begin{matrix}-3 & 5& \\ 2 & 3 & \end{matrix}\right|\left.\begin{matrix}15 & \\ -10& \end{matrix}\end{bmatrix}`

Then, Required linear system of equations: :

`-3x+5y=15\\2x+3y=-10`

∴ The correct answer is C.
`-3x+5y=15\\2x+3y=-10`