+0  
 
+1
179
3
avatar+32 

how to solve symultanious equations

 

5x+2y=-2

3x-5y=17.4

yahya  May 13, 2017
edited by yahya  May 13, 2017
Sort: 

3+0 Answers

 #1
avatar+5552 
+3

Can you give an example of one of these problems?

hectictar  May 13, 2017
 #2
avatar+6900 
+2

5x + 2y = -2 --- call this the first equation

3x - 5y = 17.4 --- call this the second equation

First equation implies that

3x + 1.2y = -1.2 --- call this the third equation

Subtract the second equation from the third equation and get:

6.2 y = -18.6

y = -3

Substitute the answer for y into the first equation and get:

5x - 6 = -2

5x = 4

x = 4/5

And done!!

MaxWong  May 15, 2017
 #3
avatar+6900 
+1

And if you want to solve a general linear simultaneous equation: (That's what we do in 8th grade...... :) )

ax + by = c --- (1)

dx + ey = f --- (2)

(1) implies that:

y = (c - ax)/b --- (3)

Substitute (3) into (2):

dx + (ec - aex)/b = f

dx + ec/b - aex/b = f

dx - aex/b = f - ec/b <---- from now on I have to use LaTeX.... Too complicated to type like that....

\(x(d - \dfrac{ae}{b})=f - \dfrac{ce}{b}\\ x = \dfrac{f - \frac{ce}{b}}{d - \frac{ae}{b}} = \dfrac{bf-ce}{bd-ae}\)

That's the general solution for x. Now let's work that out for y.

(1) implies that

\(x = \dfrac{c-by}{a}\) --- (4)

Substitute (4) into (2):

\(\dfrac{dc-bdy}{a}+ey = f\\ \dfrac{dc}{a}-y\cdot \dfrac{bd}{a} + ey = f\\ y(e-\dfrac{bd}{a})=f-\dfrac{cd}{a}\\ y = \dfrac{f-\frac{cd}{a}}{e-\frac{bd}{a}}=\dfrac{af-cd}{ae-bd}\)

Next time you see a simultaneous equation, plug those values in, done!!

MaxWong  May 15, 2017

22 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details