Samuel's Equation for solving Simultaneous equation

ax+by= c---------------1

dx+ey= f---------------2

multiply equation 1 by d and equation 2 by a , to give:

adx + bdy = cd-------3

adx + aey = af--------4

Subtract equation 4 from equation 3

bdy - aey = cd-af

simplifying, we have

y(bd-ae) = cd-af

dividing both sides by bd-ae

y(bd-ae)/bd-ae = cd-af/bd-ae

y= cd-af/bd-ae

Derivation for x

ax + by = c-----------1

dx +ey = f------------2

Multiply equation1 by e and equation 2 by b, to give

aex + bey = ce-------------------3

bdx +bey = bf-------------------4

subtract equation 4 from equation 3

aex - bdx = ce- bf

Simplify the L.H.S, we have

x(ae-bd) = ce-bf

dividing both sides by ae - bd

x = ce-bf/ae-bd

Using Samuel's equation to solve simultaneous equation

2x + 3y =5-----------1

3x + 4y =7-----------2

solve for x, using x = ce-bf/ae-bd

Note, a =2, b =3, c=5, d=3, e=4, f=7

x = 5(4) - 3(7)/2(4) - 3(3)

=20 - 21/8 - 9

=-1/-1

=1

Assignment: Solve for Y using Samuel's Formula