Systems of Linear Equations in Two Variables

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AmusingGriffin
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3 Questions

What is the solution to a system of linear equations in two variables?

A single point

What does it mean if a system of linear equations has no solution?

The lines are parallel

In a system of linear equations, what does it mean if the number of solutions is infinite?

The lines coincide

Study Notes

Solution to a System of Linear Equations in Two Variables

  • The solution to a system of linear equations in two variables is the point of intersection of the two lines, represented by the x and y values that satisfy both equations.

Characteristics of Systems with No Solution or Infinite Solutions

  • A system of linear equations has no solution if the lines are parallel and never intersect, indicating that there is no common point that satisfies both equations.
  • A system of linear equations has an infinite number of solutions if the lines are coincident, meaning they are the same line and every point on the line satisfies both equations.

Test your understanding of systems of linear equations in two variables by answering questions about their solutions, no solution scenarios, and cases with infinite solutions.

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