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

Question

asked Jul 14, 2020 109k views

2 Answers

Aldehir · Answer 1 · 2020-07-20T21:00:03+0000

Answer:

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
of the left side:

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

Now the solution of
in the system is

y=(D_y)/(D)

where
D_y is the determinant of the matrix formed by replacing
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.