Samuel's Formula For solving Simultaneous Equations

Suppose
ax + by = c----------------------------- Equation 1
dx + ey = f----------------------------- Equation 2
Using the Elimination method, to find the formula for y
ax + by = c--------------------------Equation 1 X d
dx + ey = f--------------------------Equation  2 X a
adx + bdy = cd----------------Equation 3
adx + aey = af-----------------Equation 4
subtract equation 4 from equation 3
(adx - adx) + (bdy - aey) = cd - af
bdy - aey = cd - af
make y the subject of the equation
y(bd - ae) = cd - af
Dividing both sides by bd - ae, we have
y = cd - af/bd - ae

Using the elimination method, to find the formula for x
ax + by = c---------------------------Equation 1 X e
dx + ey = f---------------------------Equation 2 X  b
aex + bey = ce-----------------------Equation 3
bdx + bey = bf-----------------------Equation 4
subtract equation 4 from equation 3
(aex - bdx) + (bey - bey) = ce - bf
aex - bdx = ce - bf
make x the subject of the equation
x(ae - bd) = ce - bf
Dividing both sides by ae - bd, we have
x = ce - bf/ae - bd
Therefore, x = ce - bf/ ae - bd and y = cd - af/ bd -ae