From the given equations
2x-4y=7" "2x−4y=7 first equation
-3x+y=12" "−3x+y=12 second equation
Equations take the form:
a_11x+b_12y=c_13a11x+b12y=c13
a_21x+b_22y=c_23a21x+b22y=c23
So that we have
a_11=2a11=2 and a_21=-3a21=−3
b_12=-4b12=−4 and b_22=1b22=1
c_13=7c13=7 and c_23=12c23=12
The formulas
Delta=[(a_11, b_12),(a_21,b_22)]=a_11*b_22-a_21*b_12
x=([(c_13, b_12),(c_23,b_22)])/([(a_11, b_12),(a_21,b_22)])=(c_13*b_22-c_23*b_12)/(a_11*b_22-a_21*b_12)
y=([(a_11,c_13),( a_21,c_23)])/([(a_11, b_12),(a_21,b_22)])=(a_11*c_23-a_21*c_13)/(a_11*b_22-a_21*b_12)
Let us solve for x and y
Delta=[(a_11, b_12),(a_21,b_22)]=a_11*b_22-a_21*b_12
Delta=[(2, -4),(-3,1)]=2*1-(-3)*(-4)=2-12=-10
x=([(c_13, b_12),(c_23,b_22)])/([(a_11, b_12),(a_21,b_22)])=(c_13*b_22-c_23*b_12)/(a_11*b_22-a_21*b_12)
x=([(7, -4),(12,1)])/([(2, -4),(-3,1)])=(7*1-12*-4)/(2*1-(-3)*(-4))=(7+48)/(-10)=55/-10
x=-5.5
y=([(a_11,c_13),( a_21,c_23)])/([(a_11, b_12),(a_21,b_22)])=(a_11*c_23-a_21*c_13)/(a_11*b_22-a_21*b_12)
y=([(2,7),( -3,12)])/([(2, -4),(-3,1)])=(2*12-(-3)*(7))/(2*1-(-3)*(-4))=(24+21)/(-10)=45/(-10)
y=-4.5
God bless...I hope the explanation is useful.
