Question

x+2y=-1 ; 2x-3y=12 (Cramer's rule)
Please tell anybody...​

Answer 1

Answer:

x+2y=-1

2x-3y=12

Multiply by 2 in equation no.1

2(x+2y=-1)

2x+4y=-2

2x-3y=12

y=10

put the value y in any equation

I put in equation no.1

x+2y=-1

x+2×10=-1

x+20=-1

x=-1-20

x=-21

x=-21

y=10

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Answer 2

Solution:-

x + 2y = -1                                    .....(i)

2x - 3y = 12                                  ....(ii)

using cramers rule

$\rm a_1=1,b_1=2\: and\: c_1 = 1$

$\rm a_1=2,b_1= -3\: and\: c_1 = -12$

$\rm x=\dfrac{D_1}{D} ,y=\dfrac{D_2}{D}$

⇒$\rm D_1=\left[\begin{array}{ccc}c_1&b_1\\c_2&b_2\\\end{array}\right]$

⇒$\rm D=\left[\begin{array}{ccc}a_1&b_1\\a_2&b_2\\\end{array}\right]$

⇒$\rm D_2=\left[\begin{array}{ccc}a_1&c_1\\a_2&c_2\\\end{array}\right]$

$\rm D_1=\left[\begin{array}{ccc}1&2\\-12&-3\\\end{array}\right]=-3-(-24)=-3+24=21$

$\rm D_2=\left[\begin{array}{ccc}1&1\\2&-12\\\end{array}\right]=-12-(2)=-12-2=-14$

$\rm D=\left[\begin{array}{ccc}1&2\\2&-3\\\end{array}\right]=-3-(4)=-7$

so

$X=\dfrac{21}{-7} = -3\: and \: Y=\dfrac{-14}{-7} = 2$