Algebra 1 Chapter 7 Flashcards
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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?

<p>infinitely many</p> Signup and view all the answers

Use multiplication to solve this system of equations: 3x + 4y = 6 and 5x + 2y = -4.

<p>(-2, 3)</p> Signup and view all the answers

Which method seems most appropriate to solve the system: 6x - 2y = -4 and y = 3x + 2?

<p>Substitution</p> Signup and view all the answers

What does 'system of equations' mean?

<p>A set of equations with the same variables.</p> Signup and view all the answers

How many solutions do intersecting lines have?

<p>Exactly one</p> Signup and view all the answers

Name the vocabulary term that means a system of equations that has an infinite number of solutions.

<p>Dependent</p> Signup and view all the answers

In which quadrant would you shade when solving for this system of equations: y < 3x + 2?

<p>The answer depends on the specific inequalities provided.</p> Signup and view all the answers

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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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!

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