what is your definition of the substitution method?

Question

I really just need math help. And maybe some tips on how to figure this out. Thanks for understanding my math problem (if you got it right).

Answer 1

Given a set of simultaneous equations,

in one equation solve for one variable in terms of the other.

Then substitute that into the other equation and solve for

the other variable.  After that, plug the value found for one

variable into one of the original equations to solve for the other.

 

Example:  Given two simultaneous equations

x + 3y = 20

2x - 5y = -10

 

In first equation solve for x in terms of y

x = 20 - 3y

 

substitute into 2nd equation

2(20-3y) - 5y = -10

40 - 6y - 5y = -10

-11y = -10 - 40

-11y = -50

y = 50/11

 

Substitute into one of the original equations to solve for x

x + 3y = 20

x + 3(50/11) = 20

x = 20 - 150/11

x = 220/11 - 150/11

x = 70/11 = 6 5/11

 

This method is expanded for systems with more than 2 variables.