Questions and Answers
Complete the second equation below so that the terms in the system align: 2y = 3x - ____.
-22
Which equation results when you add the equations?
What is the solution to the system?
(4, -5)
Which of the following shows the system with like terms aligned?
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How can subtracting the equations help you solve the system?
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What is the solution to the system?
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You could produce a pair of like terms with opposite coefficients by multiplying the first equation by what number?
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To solve the system by elimination, __________ the equations.
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What is the solution to the system?
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How could you solve this system using elimination? Check all that apply.
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How many solutions does the system have?
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What is the solution to the system?
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It takes the printer ________ min to print a black-and-white page and ________ min to print a color page.
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Explain how knowing how to find the least common multiple (LCM) can help in solving the system of equations.
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Study Notes
Solving Linear Systems by Elimination
- The system of equations includes
3x + 6y = -18and2y = 3x - 22. - Completing the second equation results in aligning terms with
-3, 2, -22.
Adding Equations
- Adding equations in a system can yield a new equation; for instance, the result can be
8y = -40.
Solutions to Systems
- One solution to a system can be
(4, -5), another is(0.5, 3), and yet another is(-2, -4). - A specific solution is also
(0, -3).
Aligning Like Terms
- Aligning like terms in a system can result in equations such as
-4x + 0.4y = -0.8and6x + 0.4y = 4.2.
Subtracting Equations
- Subtracting equations can eliminate terms, such as y-terms, making it easier to find solutions.
Multiplication for Elimination
- To create oppositional coefficients, multiply the first equation of a system by
6to produce like terms with1/2x + 3/2y = -7and-3x + 2y = -2. - If multiplied correctly, resulting equations for elimination may look like
3x + 9y = -42and-3x + 2y = -2.
Solving Through Elimination
- You can solve by multiplying the first equation by
5and the second by2, or by multiplying the first by2and the second by5and then subtracting.
System Solutions
- Systems can consistently have one solution, or multiple solutions may be possible based on the equations given.
Application of the Problem
- Given the printer scenario, the system is defined as
24b + 4c = 2 1/2and30b + 6c = 3 1/4. - The solution to the system reveals the time taken to print, where a black-and-white page takes
1/12minutes and a color page takes1/8minutes.
Least Common Multiple (LCM)
- The LCM helps in determining the right multiplication to eliminate variables, as with the system
6x - 2y = 28and8x + 3y = 14. - For elimination in the provided example, the LCM of
6and8is24, enabling multiplication of the first equation by4and the second by-3.
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Description
Test your understanding of solving linear systems using the elimination method with these flashcards. This quiz will challenge you to align terms, derive sums, and find solutions for a given system of equations.
