Question

(e) 4x = y-5;y= 2x + 1 by cramers rule ​

Answer 1

let $\rm \: 4x-y = -5 \:\:\:\:\:\;\;\;\;\;\; ....(1)$

$\rm -2x+y = 1 \:\:\:\:\:\;\;\;\;\;\; ....(2)$

$\rm$

$\rm \therefore D = \left[ \begin{array}{cc} \:4 & -1 \\ -2 & \:\:1 \end{array} \right]$

$\rm = (4\times1)-(-2\times-1)$

$\rm = 4-2 = 2$

$\rm$

$\rm D_x = \left[ \begin{array}{cc} -5 & -1 \\ \:\;1 & \:\:1 \end{array} \right]$

$\rm = (5 \times 1)-(1 \times -1)$

$\rm = -5+1$

$\rm = -4$

$\rm$

$\rm D_y = \left[ \begin{array}{cc} \:4 & -5 \\ -2 & \:\:1 \end{array} \right]$

$\rm = 4-10 = -6$

$\rm$

by Cramer's rule

$\rm x = \dfrac{D_x}{D} = \dfrac{-4}{2} = -2$

$\rm y = \dfrac{D_y}{D} = \dfrac{-6}{2} = -3$