Systems by Substitution

Solving Systems by Substitution

Another way to find the solution between two equations.

Steps:

• isolate one of the equations (get into x= or y=)

• Substitute - plug that equation into the other equation

• Solve for the remaining variable

• Take that answer and plug into the 1st equation

• Solve for the remaining variable

Multiple Choice

One equation is already isolated. Which choice shows the correct substitution?

$$2x−3y=−1$$   $$\ y=x−1$$  

• $$2x-3(x-1)=-1$$  

• $$2x-3y=x-1$$

• $$2(x-1)-3y=-1$$  

Multiple Choice

$$2x-3(x-1)=-1$$  

Solve for x

• x = - 4

• x = - 2

• x = 2

• x = 4

Multiple Choice

$$2x−3y=−1$$   $$y=x-1$$  

Plug in x = 4 . 

You can plug into either one (but I like the one that is already in y=...)   

• y = 3

• y = - 3

• y = 5

• y = - 5

Multiple Choice

What kind of solution, is (4,3)?

• No Solution

• Many Solution

• One Solution

Multiple Choice

What does a One Solution system look like?

• parallel lines

• intersecting lines

• two lines that are the same