Solver Linear System solver (using determinant)

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Source code of 'Linear System solver (using determinant)'

This Solver (Linear System solver (using determinant)) was created by by ichudov(404)

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==section input
Variable names: *[input X=x] *[input Y=y]

*[input a11=1]X + *[input a12=-1]Y = *[input b1=0]

*[input a21=1]X + *[input a22=1]Y =  *[input b2=2]

==section solution
perl

print "Solve:
{{{ system( 
  $a11\\$X + $a12\\$Y = $b1,
  $a21\\$X + $a22\\$Y = $b2 )
}}}

Any system of equations:
{{{ system( 
  a[11]*$X + a[12]*$Y = b[1],
  a[21]*$X + a[22]*$Y = b[2])
}}}

has solution
{{{ system( 
  $X = (b[1]*a[22] - b[2]*a[12])/(a[11]*a[22]-a[21]*a[12]),
  $Y = (a[11]*b[2] - a[21]*b[1])/(a[11]*a[22]-a[21]*a[12])
  )
}}}
";

my $det = $a11*$a22-$a21*$a12;
$x = ($b1*$a22 - $b2*$a12)/$det;
$y = ($a11*$b2 - $a21*$b1)/$det;

print "or

{{{ system( 
    $X = ($b1*$a22 - $b2*$a12)/($a11*$a22-$a21*$a12) = $x,
    $Y = ($a11*$b2 - $a21*$b1)/($a11*$a22-$a21*$a12) = $y
  )
}}}

($X=$x, $Y=$y}
";

==section output
x
y
==section check
 X=x Y=y a11=1 a12=-1 b1=0 a21=1 a22=1 b2=2 x=1 y=1

==section practice
perl
  $a11 = randint( 1, 3 );
  $a12 = randint( 1, 3 );
  $a21 = randint( 1, 3 );
  $a22 = randint( 1, 3 );
  my $x1 = randint( -1, 4 );
  my $x2 = randint( -1, 4 );
  $b1 = $a11*$x1 + $a12*$x2;
  $b2 = $a21*$x1 + $a22*$x2;