Question 896474
Your matrix

№	x	y	b
1	2	-3	2
2	1	-1/2	1/3
Write down the main matrix and find its determinant

№	x	y
1	2	-3
2	1	-1/2
D = 2
 
Replace the 1st column of the main matrix with the solution vector and find its determinant

№	x	y
1	2	-3
2	1/3	-1/2
D1 = 0

 
Replace the 2nd column of the main matrix with the solution vector and find its determinant

№	x	y
1	2	2
2	1	1/3
D2 = -4/3


x = D1 / D = 0 / 2 = 0
y = D2 / D = (-4/3) / 2 = -2/3

Solution set:

x= 0
y = -2/3