Question

y+2x-19=0 2x+3y+3=0 cramers rule

Answer 1

Answer:

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

2x - 3y = 12 => 2x - 3y - 12 = 0

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}then,

b

1

c

2

−b

2

c

1

x

=

a

1

c

2

−a

2

c

1

−y

=

a

1

b

2

−b

1

a

2

1

now, use it here,

equations :- x + 2y + 1 = 0

2x -3y - 12 = 0

x/{2 × (-12) - 1 × (-3)} = -y/{1 × (-12) - 1 × 2} = 1/{1 × (-3) - 2 × 2}

=> x/(-24 + 3) = -y/(-12 - 2) = 1/(-3 - 4)

=> x/-21 = -y/-14 = 1/-7

=> x = -21/-7 = 3 and y = 14/-7 = -2

hence, x = 3 and y = -2