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

1

Explanation:

took test

Answer 2

The value of y is 1

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=(|D_y|)/(|D|)=(1)/(1)=1`

Hence, value of y is 1