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

##### 1 Answer

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

Now find the value of another determinant *x*, write the constant terms from the equations. The second column elements remain the same.

Now find

Similarly find the value of a determinant *y* in the second column, write down the constant terms. The first column elements are the coefficients of *x*. Now find

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.