Solving Systems of Equations By Graphing

The Organic Chemistry Tutor
18 Jan 201805:14

Summary

TLDRIn this lesson, the instructor demonstrates how to solve a system of equations by graphing. The equations y = 2x - 3 and y = -2/3x + 5 are graphed to identify their point of intersection, which is the solution to the system. The instructor emphasizes the importance of using a large graph for clarity and walks through the process of finding key points based on the slope and y-intercept. Additionally, the solution is verified through substitution, confirming that the intersection point is (3, 3). This comprehensive approach reinforces both graphical and algebraic methods for solving equations.

Takeaways

  • 📊 Graphing is an effective method for solving systems of equations.
  • 📏 The first equation given is in slope-intercept form: y = 2x - 3.
  • 🔍 The slope of the first equation is 2, and the y-intercept is -3.
  • ⬆️ To plot the first equation, start at the y-intercept and use the slope to find additional points.
  • 📈 The second equation is y = -2/3x + 5, which also follows slope-intercept form.
  • 🎯 The y-intercept of the second equation is 5, with a slope of -2/3.
  • 🗺️ Finding the point of intersection of the two graphs provides the solution to the system of equations.
  • ✅ The point of intersection determined through graphing is (3, 3).
  • 🔄 Substitution is another method to solve for the intersection of the equations.
  • ✖️ Eliminating fractions in equations can simplify the solving process.

Q & A

  • What are the two equations being solved in this lesson?

    -The two equations are y = 2x - 3 and y = -2/3x + 5.

  • How do you determine the point of intersection when graphing two equations?

    -The point of intersection is found by graphing both equations on a coordinate plane and identifying where the two lines cross.

  • What is the slope of the first equation, and how is it used?

    -The slope of the first equation (y = 2x - 3) is 2, which indicates that for every 1 unit you move to the right on the x-axis, you move up 2 units on the y-axis.

  • What is the significance of the y-intercept in these equations?

    -The y-intercept indicates where the line crosses the y-axis. For the first equation, the y-intercept is -3, meaning it starts at the point (0, -3) on the graph.

  • How do you graph the second equation?

    -To graph the second equation (y = -2/3x + 5), start at the y-intercept of 5 on the y-axis, then use the slope of -2/3 to find additional points by moving 3 units right and 2 units down.

  • What is the calculated point of intersection for these equations?

    -The calculated point of intersection for the two equations is (3, 3).

  • What method is used to verify the solution after graphing?

    -The solution is verified using substitution by replacing y in one equation with the expression from the other equation and solving for x.

  • How do you eliminate fractions when solving the equation?

    -You can eliminate fractions by multiplying every term in the equation by a common denominator, which simplifies the calculations.

  • What does the result x = 3 indicate in the context of the equations?

    -The result x = 3 indicates the x-coordinate of the point of intersection, which is used to find the corresponding y-coordinate.

  • Why is it beneficial to draw a larger graph?

    -Drawing a larger graph allows for better visualization of the intersection point and makes it easier to plot points accurately.

Outlines

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Mindmap

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Keywords

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Highlights

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Transcripts

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相关标签
Math EducationGraphingEquationsAlgebraSlope-InterceptTarget AudienceHigh SchoolInteractive LearningStep-by-StepVisual LearningProblem Solving
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