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.

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

Step-by-step 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. $-3x+5y=15\\2x+3y=-10$