Question

2x+3y=2 x-y/2=1/2 using Cramer's rule

Answer 1

we have to solve equations 2x + 3y = 2 ; x - y/2 = 1/2 using Cramer's rule.

solution : Cramer's rule :

if two equations : a₁x + b₁y + c₁ = 0 ; a₂x + b₂y + c₂ = 0 are given then solution of system of equations is given by,

x/(b₁c₂ - c₁b₂) = -y/(a₁c₂ - c₁a₂) = 1/(a₁b₂ - b₁a₂)

here 2x + 3y = 2 ⇒2x + 3y + (-2) = 0

and x - y/2 = 1/2 ⇒2x + (-1)y + (-1) = 0

using Cramer's rule,

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

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