Question

How do I use Cramer's rule to solve the system of equations `x+2y=-1` and `2x-3y=5`?

Answer 1

First find out the value of the determinant with the coefficients of x in the first column and coefficients of y in the second column. In this case, the first column elements would be 1 and 2, and second column elements would be 2 and -3. Let the value of this determinant be `Delta`.

Now find the value of another determinant `Delta_1`, where, in the first column, in place of coefficients of x, write the constant terms from the equations. The second column elements remain the same.

Now find `Delta_1 / Delta`. This gives you the value of x.

Similarly find the value of a determinant `Delta_2`, where in place of the coefficients of y in the second column, write down the constant terms. The first column elements are the coefficients of x. Now find `Delta_2 / Delta`. This is the value of y.

Note that when you replace the coefficients of x, you solve for x and when you replace the coefficients of y, you solve for y.