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Samuel's Formula for solving
Simultaneous equations
From the general equation
ax + by = c  (1)
dx + ey = f (2)
Where a is the coefficient of x and b is
the coefficient of y; d is the coefficient of
x and e is the coefficient of f.
c and f are the constants.
 one year ago
 one year ago
Samuel's Formula for solving Simultaneous equations From the general equation ax + by = c  (1) dx + ey = f (2) Where a is the coefficient of x and b is the coefficient of y; d is the coefficient of x and e is the coefficient of f. c and f are the constants.
 one year ago
 one year ago

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bthemesandtricksBest ResponseYou've already chosen the best response.0
Using the elimination method of solving Simultaneous Equation ax + by = c  (1) multiply with d dx + ey = f  (2) multiply with a adx + bdy =cd  (3) adx + aey = af  (4) subtract equation 4 from equation 3 adx  adx + bdy  (+aey) = cd af bdy  aey = cd  af factorise the Left Hand Side y(bd  ae) = cd  af y = cd af/bdae
 one year ago

bthemesandtricksBest ResponseYou've already chosen the best response.0
Using the elimination method of solving Simultaneous Equation ax + by = c  (1) multiply with e dx + ey = f  (2) multiply with b aex + bey = ce  (3) bdx + bey = bf  (4) Subtract equation 4 from equation 3 aex  bdx + (bey  bey) = ce  bf aex  bdx = ce  bf Factorise the Left Hand Side x(ae  bd) = ce  bf x = ce  bf/ae  bd
 one year ago

bthemesandtricksBest ResponseYou've already chosen the best response.0
How does It work For example, 2x + 3y = 5 x + 4y = 5 Using Samuel's Formula a = 2 b =3 c = 5 d =1 e =4 f = 5
 one year ago

bthemesandtricksBest ResponseYou've already chosen the best response.0
x = cebf/ae  bd x = 5 (4)  3 (5)/2 (4)  3 (1) x = 20  15 / 8  3 x = 5/5 x=1 y = cd  af/ bd  ae y = 5 (1)  2 (5)/ 3 (1)  2 (4) y= 5 10/3  8 y= (5)/(5) y=1 Therefore, x =1 and y =1 You can try other questions too
 one year ago

bthemesandtricksBest ResponseYou've already chosen the best response.0
Thanks everyone please drop your comments
 one year ago

DirectrixBest ResponseYou've already chosen the best response.1
@bthemesandtricks would like to know if you have seen this formula before in another guise and if you will proof it for errors. Please respond. Thanks.
 one year ago

bthemesandtricksBest ResponseYou've already chosen the best response.0
Nah I've not seen it before. I derived the formula while in high school.
 one year ago

DirectrixBest ResponseYou've already chosen the best response.1
@bthemesandtricks With these two simultaneous equations, will you use your formula results to post the coordinates of the common solution, if it exists? System of Equations:  (2x  5y = 7) and (3x + 11y = 19)
 one year ago

bthemesandtricksBest ResponseYou've already chosen the best response.0
Perhaps. You could try it out
 one year ago

DirectrixBest ResponseYou've already chosen the best response.1
I could. I had in mind to compare my traditional solution technique answers to those of your formula.
 one year ago

bthemesandtricksBest ResponseYou've already chosen the best response.0
yeah try it out and you'll seee it works
 one year ago

CliffSedgeBest ResponseYou've already chosen the best response.0
In general, I'd use regular substitution, or if I was feeling fancy an augmented matrix or even Cramer's Rule.
 one year ago

CliffSedgeBest ResponseYou've already chosen the best response.0
It looks like what you posted is the same as Cramer's Rule.
 one year ago

CliffSedgeBest ResponseYou've already chosen the best response.0
It's a specialized case of using determinants of matrices to solve equations, but it amounts to regular substitution. For two linear equations in standard form with two unknowns, the general substitution method of solving follows the same steps every time, so it lends itself well to a single solution equation (or set of equations to be more precise) that works every time. I'd say it's analogous to how the quadratic formula is a general solution form of completing the square.
 one year ago
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