Digital SAT Math - Desmos Lesson #2 Systems of Equations

Tutorllini Test Prep
11 Nov 202205:29

TLDRIn this tutorial, Tutorlini Test Prep demonstrates how to use Desmos for solving systems of equations on the digital SAT Math section. The video explains that Desmos allows graphing equations without isolating y, making it easier to find intersections. Examples are provided, showing how to input equations and use Desmos' features to zoom and move the graph to identify solutions. The video also covers how Desmos can simplify solving linear and quadratic systems, potentially saving time on the SAT. The presenter encourages viewers to practice using Desmos and offers tutoring services for further assistance.

Takeaways

  • 📐 Desmos is a powerful tool for solving systems of equations on the SAT Math section without needing to isolate y.
  • 🔍 You can directly input equations into Desmos, even if they are not in the form of y = ..., to find intersections.
  • 🖱️ Use mouse tools like clicking and dragging to move the graph and zooming in and out to better locate intersections.
  • 🔢 For the first example, the system of equations 4x = 20 and -3x + y = -7 intersects at (5, 8), leading to the solution x + y = 13.
  • ✅ Desmos provides the exact coordinates of the intersection point, which can be used to answer related questions.
  • 🔄 For the second problem, the system 24x + y = 48 and 6x + y = 72 intersects at (-4/3, 80), focusing on the y-value for the answer.
  • 📉 Desmos is also effective for systems involving a mix of linear and quadratic equations, as demonstrated in the third example.
  • 🎯 In the third example, the linear equation y = 6x - 12 barely touches the parabola y = x^2 - 2x + 4 at (2, 0), providing a unique solution.
  • ⏰ Using Desmos can save time on the SAT, allowing test-takers to allocate more time to more challenging problems.
  • 👨‍🏫 The presenter offers tutoring services for all sections of the SAT and math subjects from 7th grade to AP/early college level.

Q & A

  • What is the main topic of the video?

    -The main topic of the video is how to use Desmos for solving systems of equations in digital SAT Math.

  • What is a key advantage of using Desmos over traditional graphing calculators for graphing equations?

    -A key advantage of Desmos is that you do not need to get 'y' by itself to graph an equation; as long as it is in terms of 'X' and 'Y', you can plug the equations directly into Desmos and look for the intersection.

  • How can you interact with the graph on Desmos during the SAT?

    -You can click and drag to move the graph around and use the scroll wheel to zoom in and out.

  • What is the solution to the system of equations 4X = 20 and -3X + Y = -7 as demonstrated in the video?

    -The solution to the system of equations is (5, 8).

  • What is the value of X + Y for the solution (5, 8) from the video?

    -The value of X + Y for the solution (5, 8) is 13.

  • What are the equations used in the second example of the video?

    -The equations used in the second example are 24X + Y = 48 and 6X + Y = 72.

  • What is the solution to the system of equations 24X + Y = 48 and 6X + Y = 72?

    -The solution to the system is (-4/3, 80).

  • How does Desmos handle systems of equations that include both linear and quadratic equations?

    -Desmos can handle systems of equations with both linear and quadratic equations in the same way, by graphing them and finding the intersection points.

  • What is the solution to the system of equations Y = X - 2 and Y = 6X - 12 as shown in the video?

    -The solution to the system is (2, 0).

  • What is the benefit of using Desmos for solving systems of equations on the SAT?

    -Using Desmos can save time on solving systems of equations that are difficult to do by hand, allowing more time to tackle tougher questions.

  • What additional services does the tutor offer as mentioned in the video?

    -The tutor offers tutoring services for all sections of the SAT and all math subjects from about 7th grade to AP/early college level.

Outlines

00:00

📐 Desmos for Solving SAT Math Systems of Equations

The speaker introduces a tutorial on using Desmos for the digital SAT Math section, focusing on systems of equations. They explain that Desmos allows for graphing equations without isolating y, simply by inputting equations in terms of x and y. The tutorial demonstrates how to input equations into Desmos and find their intersection points, which represent the solutions to the systems. The speaker walks through three examples, showing how to use Desmos to solve for the intersection points, calculate x+y, and identify the correct answer choices. They also highlight the benefits of using Desmos over traditional graphing calculators, emphasizing its utility for both known and unknown systems of equations, and its potential to save time on the SAT.

05:02

🎓 Conclusion and Call to Action for SAT Math Resources

In the concluding paragraph, the speaker summarizes the lesson and encourages viewers to like and subscribe for more digital SAT Math content. They also promote their tutoring services, offering to tutor all sections of the SAT and math subjects from 7th grade to AP or early college level. The speaker provides a link to their website in the video description for those interested in their tutoring services. They thank the viewers for watching and wish them luck with their studies.

Mindmap

Keywords

💡Desmos

Desmos is an online graphing calculator that is used for creating and exploring graphs of mathematical functions. In the context of the video, Desmos is highlighted as a tool for solving systems of equations, which is a common task in SAT Math. The tutor demonstrates how to input equations into Desmos and use its features to find the intersection points, which represent the solutions to the systems of equations.

💡Systems of Equations

A system of equations refers to a set of two or more equations that need to be solved simultaneously. In the video, the tutor is teaching viewers how to use Desmos to solve such systems, particularly those involving two variables, typically x and y. The solutions to these systems are the points where the graphs of the equations intersect.

💡Graphing

Graphing is the process of plotting the solution of a mathematical equation on a graph. In the video, graphing is used to visually represent the equations from the systems of equations. The tutor shows how to input equations into Desmos and then manipulate the graph to find the points of intersection, which are the solutions to the equations.

💡Intersection

In the context of the video, intersection refers to the point where two or more graphs (representing equations) meet. This is significant because the intersection point(s) of the graphs in a system of equations are the solutions to that system. The tutor uses Desmos to find these points by zooming and panning the graph.

💡Zoom In/Out

Zooming in and out are actions used in Desmos to adjust the scale of the graph for better visibility of the intersection points. The tutor mentions using the scroll wheel to zoom in and out, which helps in identifying the exact points where the graphs intersect, especially when the intersection is not immediately clear.

💡Scroll Wheel

The scroll wheel is a feature on a mouse that allows for scrolling up and down on a webpage or application. In the video, the tutor advises bringing a mouse with a scroll wheel to the test day to use for zooming in and out on the graph in Desmos, which is essential for accurately identifying the solutions to the systems of equations.

💡Linear Equations

Linear equations are equations that represent straight lines when graphed. The video includes examples of systems of equations where both equations are linear. The tutor demonstrates how to input these into Desmos and find their intersection points, which are the solutions to the system.

💡Quadratic Equations

Quadratic equations are equations that represent parabolas when graphed. The video includes an example of a system of equations where one equation is quadratic and the other is linear. The tutor shows how to use Desmos to find the intersection point of such a system, which can be more challenging than linear systems due to the curved nature of the parabola.

💡Solution

In the context of systems of equations, a solution is the set of values for the variables that satisfy all the equations in the system. The tutor uses Desmos to find these solutions by identifying the intersection points of the graphs. For example, the solution '5 comma 8' refers to the point (5, 8) where the x-coordinate is 5 and the y-coordinate is 8.

💡SAT Math

SAT Math is a section of the SAT (Scholastic Assessment Test) that assesses students' mathematical problem-solving skills. The video is focused on preparing for this section by teaching how to use Desmos to solve systems of equations, which is a common type of problem in the SAT Math section.

Highlights

Desmos allows graphing equations without isolating y, as long as they are in terms of x and y.

Desmos is advantageous over physical graphing calculators for digital SAT Math.

Equations can be directly input into Desmos to find intersections for system solutions.

Use mouse to navigate and zoom in Desmos for better visibility of graph intersections.

Example problem: 4x = 20 and -3x + y = -7, intersection found at (5,8).

For x + y, sum the coordinates of the intersection point for the answer.

Second example: 24x + y = 48 and 6x + y = 72, intersection at (-1.33, 80).

Desmos can solve for y values in system equations.

Third example involves a linear and quadratic system: y = x - 2 and y = 6x - 12.

Intersection of linear and quadratic systems can be found using Desmos.

Desmos is a powerful tool for solving various types of system equations.

Desmos can save time on problems that are solvable by hand, allowing focus on tougher questions.

The tutorial covers how to use Desmos for the digital SAT Math section.

Desmos is recommended for its ease of use and effectiveness in solving systems of equations.

The tutor offers services for tutoring all sections of the SAT and math subjects.

The video concludes with a call to like, subscribe, and check the description for tutoring services.