Question

Using Cramer's Rule, what is the value of y in the solution to the system of linear equations below?

9x-2y - 5
-3x-4y=-4

Answer 1

The answer is B!

Explanation:

Edge 2021 :)

Answer 2

The second choice.

Explanation:

We first write the system of equations as an augmented matrix:

`\left(\begin{array}c 9 & -2 & 5\\ -3 & -4 & -4 \end{array}\right)`

Then we take the determinant
`D` of the left side:

`D=\begin{vmatrix}9 & -2 \\ -3 & -4 \\ \end{vmatrix} =(9)(-4)-(-2)(-3)=-42`

Now the solution of
`y` in the system is

`y=(D_y)/(D)`

where
`D_y` is the determinant of the matrix formed by replacing
`y` column of the left matrix with elements of the right matrix
`(5, -4)`:

`D_y=\begin{vmatrix}9 & 5 \\ -3 & -4 \\ \end{vmatrix}=(9)(-4)-(5)(-3)=-21`

therefore,

`y=\frac{\begin{vmatrix}9 & 5 \\ -3 & -4 \\ \end{vmatrix}}{D}`

`\boxed{y=\frac{\begin{vmatrix}9 & 5 \\ -3 & -4 \\ \end{vmatrix}}{-42} =(-21)/(-42) =(1)/(2)}`

which is the second choice.