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Questions and Answers
What is the solution to a system of linear equations in two variables?
What is the solution to a system of linear equations in two variables?
- A circle
- A single point (correct)
- A parabola
- A line
What does it mean if a system of linear equations has no solution?
What does it mean if a system of linear equations has no solution?
- The lines intersect at multiple points
- The lines are parallel (correct)
- The lines intersect at one point
- The lines coincide
In a system of linear equations, what does it mean if the number of solutions is infinite?
In a system of linear equations, what does it mean if the number of solutions is infinite?
- The lines are parallel
- The lines intersect at multiple points
- The lines intersect at one point
- The lines coincide (correct)
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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.
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