Question

x+2y=-1;2x-3y=12.. solve the following simultaneous equations using Cramer rule​

Answer 1

Step-by-step explanation:

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}

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)

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

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

hence, x = 3 and y = -2

Answer 2

Step-by-step explanation:

Now,

x+2y = -1

a1=1 b1=2 c1 = -1

Also,

2x-3y=12

a2=2 b2= -3 c2=12

D = |a1 b1 | |1 2| = (1×-3) - (2×2)

|a2 b2| |2 -3| = (-3) - (4)

= -3 -4

= -7

Dx = |c1 b1 | |-1 2 | = (-1×-3) - (2×12)

|c2 b2| |12 -3| = (3) - (24)

= 3-24

= -21

Dy = |a1 c1 | | 1 -1| = (1×12) - (-1×2)

|a2 c2| |2 12| = (12) + (2)

= 14

x = Dx/D = -21/-7 = 3/1 x=3

y = Dy/D = 14/-7 = -2/1 y=-2