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

Answer:

The second choice.

Step-by-step explanation:

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

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

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

$y=\frac{D_y}{D}$

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,

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

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

which is the second choice.

Answer 2

Answer:

The answer is B!

Step-by-step explanation:

Edge 2021 :)