What is the geometric interpretation of the solution to a system of linear equat

Practice Questions

Q1
What is the geometric interpretation of the solution to a system of linear equations in two variables?
  1. The point where the two lines intersect.
  2. The area enclosed by the lines.
  3. The distance between the lines.
  4. The slope of the lines.

Questions & Step-by-Step Solutions

What is the geometric interpretation of the solution to a system of linear equations in two variables?
  • Step 1: Understand that a system of linear equations in two variables consists of two equations, each representing a line on a graph.
  • Step 2: Each equation can be written in the form y = mx + b, where m is the slope and b is the y-intercept.
  • Step 3: When you graph both lines on the same coordinate plane, you will see two lines that may intersect at a point.
  • Step 4: The point where the two lines intersect is the solution to the system of equations.
  • Step 5: This intersection point represents the values of the two variables that satisfy both equations at the same time.
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