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How do we use determinants for solving a system of linear equations?

Solution

For solving an equation using determinants we use cramer\'s rule.

For a system of linear equations with two variable ,

Let the system of equations be ax+by=R and cx+dy=S

to find the value of x and y we have specific formula

x=D_x/D and y=D_y/D

so we need to calculate D, Dx and Dy.

the matrix for D becomes

and D= (a x d)-( b x c).

The matrix for Dx becomes

and Dx = (b X S) - (d x R)

similarly the matrix for Dy becomes

and Dy= (a x S) - (c x R)

Find the vaules of D, Dx and Dy and put it in the formula you will get the vaule of x and y via deteminant method.