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 in digital SAT Math. The video highlights the ease of graphing equations without isolating y, simply by inputting them into Desmos and finding intersections. Three examples are covered, showcasing the process for linear and quadratic systems. The presenter zooms in and out to pinpoint solutions, emphasizing Desmos as a powerful tool for time-saving and tackling complex problems. The video concludes with a call to action for viewers to like, subscribe, and consider tutoring services for comprehensive SAT and math support.

Takeaways

  • 📐 Desmos is a powerful tool for solving systems of equations on the digital SAT Math section.
  • 🔍 You don't need to isolate y to graph an equation on Desmos, as long as it's in terms of x and y.
  • 🖥️ Desmos allows you to simply input equations and find their intersection points for solutions.
  • 🔎 Use the mouse to drag and scroll to navigate and zoom in/out on the graph for better visibility.
  • ✅ The intersection point gives you the solution to the system of equations.
  • 📝 For the first example, the solution is (5, 8) and x + y equals 13, leading to answer choice C.
  • 🧐 In the second example, the solution is (-4/3, 80), and the y-value is 80, which is the final answer.
  • 📉 Desmos works for linear and quadratic systems; the method remains the same for different types of equations.
  • 🕵️‍♂️ Zooming in closely can help identify points of intersection that might appear to be just grazing the curve.
  • 💡 Desmos can save time on problems that are solvable by hand, allowing more time for tougher questions.
  • 🌟 The tutorial suggests that using Desmos can be a time-saving strategy during the SAT Math section.

Q & A

  • What is the main advantage of using Desmos for graphing equations compared to physical graphing calculators?

    -Desmos allows you to graph an equation without needing to solve for y by itself, as long as the equation is in terms of X and Y.

  • How does Desmos help in finding the solution to a system of equations?

    -Desmos helps by allowing you to input the equations and visually identify their intersection point, which is the solution to the system.

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

    -The solution is the point of intersection, which Desmos indicates as (5, 8).

  • How can you interact with the graph on Desmos to better visualize the intersection of equations?

    -You can click and drag to move the graph around and use the scroll wheel to zoom in and out for a clearer view of the intersection.

  • What is the sum of x and y for the solution (5, 8) from the first example in the video?

    -The sum of x and y is 5 + 8, which equals 13.

  • In the second example, what is the y-value of the solution to the system of equations 24x + y = 48 and 6x + y = 72?

    -The y-value of the solution is 80.

  • How does Desmos handle systems of equations with different types of functions, such as linear and quadratic?

    -Desmos can handle systems with linear and quadratic functions in the same way, by graphing both and finding their intersection.

  • What is the solution to the system involving the quadratic equation y = x^2 - 2x + 4 and the linear equation y = 6x - 12 as shown in the video?

    -The solution is the point (2, 0), which is the intersection of the parabola and the line.

  • What additional benefit does using Desmos provide for solving systems of equations on the SAT?

    -Using Desmos can save time on solving systems of equations, allowing more time to tackle tougher questions that require more thought and calculation.

  • What services does the tutor offer according to the video description?

    -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

This paragraph introduces a tutorial on using Desmos for solving systems of equations on the digital SAT Math test. The instructor explains that Desmos allows for graphing equations without isolating y, as long as they are in terms of x and y. The tutorial demonstrates solving two systems of equations by graphing and finding the intersection points. The first system is a simple linear system, and the second one involves a linear and quadratic equation. The instructor also advises bringing a mouse for test day to navigate the graph more effectively. The solutions are found by zooming in and clicking on the intersection points, with Desmos providing the coordinates of the solutions.

05:02

🔍 Conclusion and Tutoring Services Offered

The final paragraph wraps up the lesson by encouraging viewers to like and subscribe for more digital SAT Math content. The instructor offers personal tutoring services for all sections of the SAT and math subjects from 7th grade to AP or early college level. A link to the instructor's website is provided in the video description for those interested in tutoring. The instructor thanks viewers for watching and wishes them luck with their studies.

Mindmap

Keywords

💡Desmos

Desmos is an online graphing calculator that is used for creating graphs of mathematical functions and equations. In the context of the video, Desmos is highlighted as a powerful tool for solving systems of equations without the need for isolating variables, which simplifies the process of finding intersections on a graph. The tutor demonstrates how to input equations into Desmos and use its features to identify the points of intersection, which represent the solutions to the systems of equations presented in the video.

💡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 uses Desmos to solve systems of linear equations, which are equations that involve two variables and can be represented as straight lines on a graph. The solutions to these systems are the points where the lines intersect, and Desmos makes it easy to visualize and find these points.

💡Graphing Calculator

A graphing calculator is a specialized device that is used to graph functions and solve complex mathematical problems. The video contrasts Desmos with traditional physical graphing calculators, emphasizing that Desmos allows for graphing equations without the need to rearrange them to solve for a single variable, which is often necessary with physical calculators.

💡Intersection

In the context of graphing equations, an intersection refers to the point where two or more graphs meet. The video explains that finding the intersection points of the graphs of equations in a system is key to solving the system. Desmos helps identify these points by allowing users to zoom in and click on the point of intersection to get the exact coordinates.

💡Zoom In/Out

Zooming in and out are actions used in graphing tools to adjust the scale of the graph for better visibility. In the video, the tutor demonstrates how to use the zoom feature in Desmos to get a closer look at the intersection points of the equations, which is crucial for accurately identifying the solutions to the systems of equations.

💡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 mentions using the scroll wheel to zoom in and out of the graph in Desmos, which is an essential technique for focusing on the area of intersection between the equations' graphs.

💡Linear Equations

Linear equations are equations that describe straight lines and are typically in the form of y = mx + b, where m is the slope and b is the y-intercept. The video includes examples of linear equations and demonstrates how to input and solve them using Desmos, highlighting that Desmos can handle both linear and non-linear equations.

💡Quadratic Equations

Quadratic equations are a type of polynomial equation that has the form ax^2 + bx + c = 0, where a, b, and c are constants. The video includes a system of equations where one of the equations is quadratic, and the tutor shows how Desmos can be used to find the intersection with a linear equation, even when the equations have different degrees.

💡Digital SAT Math

Digital SAT Math refers to the section of the SAT exam that involves mathematical problems that can be solved using digital tools. The video is part of a series aimed at preparing students for this part of the test, focusing on how to use Desmos to solve systems of equations, which is a common type of problem in the SAT Math section.

💡Tutoring Services

Tutoring services are educational support provided by tutors to help students understand and master academic subjects. The video concludes with a mention of the tutor's services, indicating that they offer help with all sections of the SAT and various math subjects, suggesting that the use of Desmos and other strategies taught in the video could be part of the tutoring provided.

Highlights

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

Desmos is advantageous for digital SAT Math as it simplifies graphing systems of equations.

To find solutions, look for the intersection of graphs on Desmos.

Use Desmos to input equations directly for solving systems of equations.

Zoom and drag features in Desmos help in locating the intersection points.

Desmos provides the exact coordinates of intersection points.

For the given example, Desmos shows the solution (5,8) for the system of equations.

Desmos can be used to solve for x+y by substituting the values from the solution.

Desmos is effective for solving linear and quadratic systems alike.

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

The video demonstrates solving a system with 24x + y = 48 and 6x + y = 72 using Desmos.

Desmos indicates the solution for the second example as -1.33, 80.

Desmos can be used to solve systems involving a quadratic and a linear equation.

For the third example, Desmos shows a single intersection at (2,0).

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

The tutorial concludes with an encouragement to like, subscribe, and consider the tutor's services for SAT Math.

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