How do you solve a system of equations using substitution?

• A. By graphing both equations
• B. By solving one equation for one variable and substituting into the other
• C. By adding both equations together
• D. By using elimination methods

Answer: (B)

To solve a system of equations using substitution, the key process involves isolating one variable in one of the equations and then replacing that variable with the expression derived from that isolation in the other equation. This method allows you to transform the system into a single equation with one variable, which can then be solved more easily.

For example, consider a system like:

1. ( x + y = 10 )

2. ( 2x - y = 4 )

By isolating ( y ) in the first equation, you can rewrite it as ( y = 10 - x ). This substitution transforms the second equation into:

( 2x - (10 - x) = 4 )

Now you have a single-variable equation, which can be solved more simply. Once you find the value of ( x ), you can substitute it back into either of the original equations to find the corresponding ( y ) value.

This method is particularly useful when one equation is easily manipulated to isolate a variable, making it a preferred technique in many scenarios. It stands in contrast to other methods, such as graphing, elimination, or simply adding equations, which may not be as direct or effective depending on the nature of the equations