Question

Given the system of equations, what is the value of the system determinant?

2x + y = 8
x - y = 10
0-1
0-2
0-3

Answer 1

-3

Explanation:

2x+-3=8

x-3=10

Answer 2

Given:

The system of equation is

`2x+y=8`

`x-y=10`

To find:

The value of the system determinant.

Solution:

If two equations of a system of equations are
`a_1x+b_1y=c_1` and
`a_2x+b_2y=c_2`, then the system determinant is

`D=\left|\begin{matrix}a_1&b_1\\a_2&b_2\end{matrix}\right|`

`D=a_1b_2-b_1a_2`

The given two equations are
`2x+y=8` and
`x-y=10`.

Here,
`a_1=2,b_1=1,c_1=8, a_2=1,b_2=-1,c_2=10`.

`D=\left|\begin{matrix}2&1\\1&-1\end{matrix}\right|`

`D=(2)(-1)-(1)(1)`

`D=-2-1`

`D=-3`

The value of the system determinant is -3. Therefore, the correct option is C.