Question

2x+3y=2 ; x-y/2=1/2 Solve this equations by Cramer’s method.

Answer 1

according to Cramer's rule,
when two equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 .
$then, \frac{x}{b_1c_2-b_2c_1}=\frac{-y}{a_1c_2-a_2c_1}=\frac{1}{a_1b_2-b_1a_2}$

Given, 2x + 3y - 2 = 0
x - y/2 = 1/2 => 2x - y = 1 => 2x -y - 1 = 0

x/{3 × (-1) - (-2) × (-1)} = -y/{2 × (-1) - (-2) × 2} = 1/{2 × (-1) - 3 × 2 }

=> x/(-3 - 2) = -y/(-2 + 4) = 1/(-2 - 6)

=> x/(-5) = -y/2 = /1-8

=> x = 5/8 and y = 1/4