Question

while solving the given simultaneous equations by cramer's method, the determinants D, Dx and Dy were obtained as follows.

Answer 1

The equations are 2x + 3y = 4 and x + 2y = 5.

• If the equations are

                        $a_{1}x+b_{1}y=c_{1}----------(1)$

                        $a_{2}x+b_{2}y=c_{2}----------(2)$

        Then

                 $D=\left|\begin{array}{cc}a_{1} &b_{1}\\a_{2} &b_{2}\\\end{array}\right|$   $D_{x} =\left|\begin{array}{cc}c_{1} &b_{1}\\c_{2} &b_{2}\\\end{array}\right|$  $D_{y} =\left|\begin{array}{cc}a_{1} &c_{1}\\a_{2} &c_{2}\\\end{array}\right|$   --------(3)

• Given,

                $D=\left|\begin{array}{cc}2&3\\1&2\\\end{array}\right|$     $D_{x} =\left|\begin{array}{cc}4&3\\5&2\\\end{array}\right|$    $D_{y} =\left|\begin{array}{cc}2&4\\1&5\\\end{array}\right|$        ----------(4)

• Comparing (3) and (4), we get

               $a_{1}=2,b_{1}=3,c_{1}=4$

               $a_{2}=1,b_{2}=2,c_{2}=5$

• Substituting above values in (1) and (2), we get

                2x + 3y = 4

                  x + 2y = 5

Answer 2

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