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Questions and Answers
Solve this system of equations: 3x - 5y = -16 and 2x + 5y = 31.
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?
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.
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?
When solving the system of equations x + 3y = 3 and 2x + 6y = 6, how many solutions will you get?
Use multiplication to solve this system of equations: 3x + 4y = 6 and 5x + 2y = -4.
Use multiplication to solve this system of equations: 3x + 4y = 6 and 5x + 2y = -4.
Which method seems most appropriate to solve the system: 6x - 2y = -4 and y = 3x + 2?
Which method seems most appropriate to solve the system: 6x - 2y = -4 and y = 3x + 2?
What does 'system of equations' mean?
What does 'system of equations' mean?
How many solutions do intersecting lines have?
How many solutions do intersecting lines have?
Name the vocabulary term that means a system of equations that has an infinite number of solutions.
Name the vocabulary term that means a system of equations that has an infinite number of solutions.
In which quadrant would you shade when solving for this system of equations: y < 3x + 2?
In which quadrant would you shade when solving for this system of equations: y < 3x + 2?
Flashcards
System of Equations
System of Equations
A set of two or more equations with the same variables.
Solution to a System
Solution to a System
A set of values for the variables that satisfy all equations in the system.
Substitution Method
Substitution Method
Solving a system by substituting the expression for one variable from one equation into the other.
Infinite Solutions (System)
Infinite Solutions (System)
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Intersecting Lines
Intersecting Lines
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Dependent Equations
Dependent Equations
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Solving by Multiplication
Solving by Multiplication
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Solving a System of Equation
Solving a System of Equation
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x values in a system
x values in a system
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Solving System (Substitution)
Solving System (Substitution)
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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.
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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!
