Ordered pair solutions to equations | Graphing lines and slope | Algebra Basics | Khan Academy

TL;DR

Determine if 3, -4 is a solution to the equation 5x + 2y = 7 through both substitution and graphing methods.

Transcript

Is 3 comma negative 4 a solution to the equation 5x plus 2y is equal to 7? So there's two ways to think about it. One, you could just substitute this x and y value into this equation to see if it satisfies-- and then we'll do that way first-- and the other way is if you had a graph of this equation, you could see if this point sits on that graph, w... Read More

Key Insights

• 😥 Two methods, substitution and graphing, are used to determine if a point is a solution to an equation.
• 🙃 Substituting values into the equation and evaluating both sides checks for equality.
• 😥 Graphing the equation visually confirms if a point lies on the line of the equation.

Questions & Answers

Q: How can you determine if a point is a solution to an equation?

There are two methods - substitution and graphing. By substituting the x and y values into the equation and evaluating both sides, you can check for equality. Another way is by graphing the equation and observing if the point lies on the line.

Q: Was 3, -4 identified as a solution through substitution?

Yes, when substituting 3 for x and -4 for y in the equation 5x + 2y = 7, the left side simplifies to 15 - 8 which equals 7, confirming that 3, -4 is a solution.

Q: How is graphing used to determine if 3, -4 is a solution?

The equation 5x + 2y = 7 is plotted on a graph, and the point 3, -4 is observed to lie on the line. By visually examining the graph, it can be confirmed that 3, -4 is a solution.

Q: Why is it important to use substitution rather than just relying on graph inspection?

Substitution ensures accurate verification of solutions, avoiding any potential errors due to imprecision or approximation. Graphs can be misleading, and slight deviations from a point's coordinates may not be noticeable, making substitution a more reliable method.

Summary & Key Takeaways

• The content explores two methods to determine if 3, -4 is a solution to the equation 5x + 2y = 7: substitution and graphing.

• By substituting the values of x and y into the equation, the left side simplifies to 15 - 8, which equals 7. Therefore, 3, -4 is a solution.

• Graphically, the equation is plotted on a graph, and it is observed that the point 3, -4 lies on the line.