Question

Using cramer’s rule, what is the value of y in the system of linear equations below? 2x-y=3 5x-2y=8

Answer 1

The answer is y=2×-3 and y=4-5/2x

Answer 2

Answer:

The value of y is 1

Step-by-step explanation:

Given the system of linear equations

2x-y=3

5x-2y=8

we have to find the value of y using cramer’s rule

Cramer’s Rule is a method that uses determinants to solve the systems of equations that have same number of equations as that of variables.

The coefficient matrix is

$D=\begin{bmatrix}2&-1\\5&-2\end{bmatrix}$

$|D|=\begin{vmatrix}2&-1\\5&-2\end{vmatrix}=-4(-5)=-4+5=1$

For Y-matrix

$D_y=\begin{bmatrix}2&3\\5&8\end{bmatrix}$

$|D_y|=\begin{vmatrix}2 & 3\\5 & 8\end{vmatrix}=16-15=1$

By cramer's rule

$y=\frac{|D_y|}{|D|}=\frac{1}{1}=1$

Hence, value of y is 1