your first problem is:
x + 2y = 2
3x + y = 3
you set up a matrix as shown below:
1 2 | 2
3 1 | 3
cramer's rule says:
x = Dx / D
y = Dy / D
first you want to find D.
That's the left part or our matrix which is equal to:
1 2
3 1
the value for D is equal to 1*1 - 2*3 = 1 - 6 = -5
next we want to find Dx
Dx is found by replacing the first column in D with the result column.
the matrix for Dx becomes:
2 2
3 1
the value for Dx is equal to 2*1 - 2*3 = 2 - 6 = -4
next we want to find Dy
Dy is found by replacing the second column in D with the result column.
the matrix for Dy becomes:
1 2
3 3
the value for Dy is equal to 1*3 - 2*3 = 3 - 6 = -3
we have:
D = -5
Dx = -4
Dy = -3
we now solve for x and y as follows:
x = Dx / D = -4 / -5 = 4/5
y = Dy / D = -3 / -5 = 3/5
our final answer is:
x = 4/5
y = 3/5
i will solve this system of equations the standard way to confirm that these answers are what we should expect.
the original equations are:
x + 2y = 2
3x + y = 3
multiply the second equation by -1 to get:
x + 2y = 2
-6x - 2y = -6
add these equations together to get:
-5x = -4
divide both sides of this equation by -5 to get:
x = 4/5
substitute 4/5 for x in the first equation to get:
x 2y = 2
this becomes:
4/5 + 2y = 2
subtract 4/5 from both sides of this equation to get:
2y = 2 - 4/5
simplify to get:
2y = 6/5
divide both sides of this equation by 2 to get:
y = 6/5 * 1/2
this becomes:
y = 3/5
our answer doing it the conventional way are:
x = 4/5
y = 3/5
this agrees with our answer that we derives using cramer's rule, so the rule is confirmed as being accurately processed.
you should be able to do the rest on your own.
let me know if you have problems.
