Question

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

Answer 1

Answer:

-3

Step-by-step 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.