Graphing systems of equations | Systems of equations | 8th grade | Khan Academy

TL;DR

This video explains how to solve a system of linear equations by graphing, using two given equations.

Transcript

Solve the system of linear equations by graphing, and they give us two equations here. 5x plus 3y is equal to 7, and 3x minus 2y is equal to 8. When they say, "Solve the system of linear equations," they're really just saying find an x and a y that satisfies both of these equations. And when they say to do it by graphing, we're essentially going to... Read More

Key Insights

• 🫥 Solving a system of linear equations by graphing involves finding the point of intersection between two lines.
• 🫥 Two points are sufficient to graph a line accurately.
• 🏙️ The x- and y-intercepts help in determining points on the lines.
• 📈 Verifying the solution obtained from graphing ensures its accuracy.
• ❓ Graphing provides a visual representation of the solution to a system of linear equations.
• 👋 Hand-drawn graphs may not be precise but can still give a good approximation of the solution.
• ❣️ The point of intersection represents the values for x and y that satisfy both equations.

Questions & Answers

Q: What is the purpose of solving a system of linear equations by graphing?

Solving a system of linear equations by graphing helps find the point of intersection, which represents the solution to the equations. It visually demonstrates where the two lines cross, making it easy to identify the solution.

Q: How many points do we need to graph a line?

Only two points are needed to graph a line. By selecting two different values for x and solving for y, we can plot these points and draw a straight line connecting them.

Q: What do the x- and y-intercepts represent in the context of an equation?

The x-intercept is the point at which the graph intersects the x-axis, where y = 0. Similarly, the y-intercept is the point at which the graph intersects the y-axis, where x = 0. These intercepts help in graphing the line accurately.

Q: Why is it important to verify the solution obtained from graphing?

Verifying the solution obtained from graphing is crucial to ensure that it satisfies both equations. By substituting the x and y values into each equation, we can confirm that the solution is accurate.

Summary & Key Takeaways

• The video demonstrates the process of solving a system of linear equations by graphing.

• Two equations are given: 5x + 3y = 7 and 3x - 2y = 8.

• The first step is to graph each equation and find the point where they intersect, which represents the solution to the system.