Notes: Solving System of Equations by Elimination
Notes: Solving System of Equations by Elimination
SOL A1.4e
Name______Date______
The Addition and Subtraction Properties of Equality can be used to solve a system of equation. Using
this method is called the ______
This is done by______
______
From there, ______
______
1.
Procedures / /Make sure both equations are in Standard Form (______)
While in standard form, which terms have the same coefficients
______
Including the operation in front of each term, what operation would cancel out those terms?
______
The remaining variable equals
______
Substitute the value of the variable above into either original equation to solve for the remaining unknown variable.
What did that variable equal?
______
a)What is/are the solutions to the system? ______
b)If graphed, what type of lines would this system form and how can you determine this WITHOUT graphing the system? ______
2)
Procedures / /Make sure both equation are in
Standard Form:
(______)
While in standard form, which terms have the same coefficients?
______
Including the operation in front of each term, what operation would cancel out those terms?
______
The remaining variable equals
______
Substitute the value of the variable above into either original equation to solve for the remaining unknown variable.
What did that variable equal?
______
a)What is/are the solutions to the system? ______
b)If graphed, what type of lines would this system form and how can you determine this WITHOUT graphing the system? ______
c)Solve both equations for y and graphing with your calculator. Is the solution set correct? ______
3)
Procedures / /Make sure both equations in Standard Form:
______/ But, what is different about this system when in Standard Form?
______
Pick a variable to eliminate: ___
(It doesn’t matter which one you choose.)
What is the least common multiple of both coefficients of those terms? _____
Multiply each equation by a number so the chosen variable to eliminate can have the same coefficients as the LCD.
(you may only need to multiply one equation) / Original System Equivalent System with like Coefficients
4x + y = 3 ______
-x - 2y = 8 ______
Decide what operation should now be used to eliminate the y term and complete.
Substitute the value of the variable above into one of the original equations to solve for the remaining unknown variable.
What did that variable equal?
______
a)What is/are the solutions to the system? ______
b)If graphed, what type of lines would this system form and how can you determine this WITHOUT graphing the system? ______
4) Procedures / /
Make sure both equations in Standard Form:
______
Pick a variable to eliminate: ___
(It doesn’t matter which one you choose.)
What is the least common multiple of both coefficients of those terms? _____
Multiply each equation by a number so the chosen variable to eliminate can have the same coefficients as the LCD.
(you may only need to multiply one equation) / Original System Equivalent System with like Coefficients
2x + 5y = -22 ______
10x + 3y = 22 ______
Decide what operation should now be used to eliminate the y term and complete.
a)What is/are the solutions to the system? ______
b)If graphed, what type of lines would this system form and how can you determine this WITHOUT graphing the system? ______
5) Procedures / /
Make sure both equations in Standard Form:
______
While in standard form, which terms has the same coefficient?
______
What operation would cancel out those terms?
______/ Original System Equivalent System with like Coefficients
x + y = 3 ______
2x + 2y = 6 ______
Decide what operation should now be used to eliminate the y term and complete.
a)What is/are the solutions to the system? ______
b)If graphed, what type of lines would this system form and how can you determine this WITHOUT graphing the system? ______
6) Procedures / /
Make sure both equations in Standard Form:
______
While in standard form, which terms has the same coefficient?
______
What operation would cancel out those terms?
______/ Original System Equivalent System with like Coefficients
-3x + y = 1 ______
3x - y = 6 ______
Decide what operation should now be used to eliminate the y term and complete.
a)What is/are the solutions to the system? ______
b)If graphed, what type of lines would this system form and how can you determine this WITHOUT graphing the system? ______