Questions and Answers
Solve this system of equations: 3x - 5y = -16 and 2x + 5y = 31.
(3, 5)
What does 'x' equal in this system of equations: y = 3x and x + 2y = -21?
-3
Solve this system of equations using substitution: x + 5y = -3 and 3x - 2y = 8.
(2, -1)
When solving the system of equations x + 3y = 3 and 2x + 6y = 6, how many solutions will you get?
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Use multiplication to solve this system of equations: 3x + 4y = 6 and 5x + 2y = -4.
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Which method seems most appropriate to solve the system: 6x - 2y = -4 and y = 3x + 2?
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What does 'system of equations' mean?
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How many solutions do intersecting lines have?
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Name the vocabulary term that means a system of equations that has an infinite number of solutions.
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In which quadrant would you shade when solving for this system of equations: y < 3x + 2?
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Study Notes
Solving Systems of Equations
- To solve the system of equations (3x - 5y = -16) and (2x + 5y = 31), find (x) and (y): the solution is (3, 5).
- For the equations (y = 3x) and (x + 2y = -21), solving for (x) reveals that (x = -3).
- The substitution method applied to (x + 5y = -3) and (3x - 2y = 8\ yields the solution (2, -1).
Nature of Solutions
- The equations (x + 3y = 3) and (2x + 6y = 6\ have infinitely many solutions, indicating they represent the same line.
- Intersecting lines represent a system with exactly one solution.
- A system classified as dependent features an infinite number of solutions.
Methods of Solving
- For the equations (6x - 2y = -4) and (y = 3x + 2), substitution is the most appropriate method.
- Multiplication can also be used for systems like (3x + 4y = 6) and (5x + 2y = -4), leading to the solution (-2, 3).
General Concepts
- A system of equations consists of multiple equations sharing the same variables.
- Knowledge of quadrants is essential when graphing inequalities or solutions on a coordinate plane.
Studying That Suits You
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Description
Test your understanding of systems of equations with these flashcards from Algebra 1 Chapter 7. Each card presents a different problem, including methods like substitution and solving for x and y. Challenge yourself and solidify your grasp on these critical algebra concepts!
