key term - Intersection Point

Definition

The intersection point is the point where two or more lines, curves, or functions meet and share a common coordinate. It represents the solution to a system of equations, where the values of the variables satisfy all the equations simultaneously.

5 Must Know Facts For Your Next Test

1. The intersection point represents the unique solution to a system of equations, where the values of the variables satisfy all the equations simultaneously.
2. Graphing a system of equations is a common method for finding the intersection point, as it allows you to visually identify the point where the lines or curves intersect.
3. The substitution method of solving a system of equations involves isolating a variable in one equation and substituting it into the other equation to find the intersection point.
4. The intersection point is essential for solving real-world applications involving systems of equations, such as finding the point of intersection between supply and demand curves or the point where two objects meet.
5. The coordinates of the intersection point are the values of the variables that satisfy all the equations in the system, and these values represent the solution to the system.

Review Questions

• Explain how the intersection point is used to solve a system of equations by graphing.
  • When solving a system of equations by graphing, the intersection point represents the solution to the system. By plotting the equations on a coordinate plane, the point where the lines or curves intersect is the intersection point, and the coordinates of this point are the values of the variables that satisfy all the equations in the system. The intersection point is the common solution that makes all the equations true simultaneously.
• Describe the role of the intersection point in solving applications with systems of equations.
  • In real-world applications involving systems of equations, the intersection point is crucial for finding the solution. For example, in a problem where two companies are competing to sell a product, the intersection point of their supply and demand curves represents the equilibrium price and quantity where the market is in balance. Similarly, in a problem involving the motion of two objects, the intersection point of their position functions represents the location where the objects meet. The intersection point provides the values of the variables that satisfy all the constraints in the application.
• Analyze how the substitution method can be used to find the intersection point of a system of equations.
  • The substitution method of solving a system of equations involves isolating a variable in one equation and substituting its expression into the other equation(s). By doing so, the system is reduced to a single equation with a single variable, which can be solved to find the value of that variable. This value can then be substituted back into one of the original equations to find the value of the other variable, resulting in the coordinates of the intersection point. The substitution method allows for the efficient determination of the intersection point without the need for graphing, making it a useful technique for solving systems of equations.

Related terms

System of Equations:

A set of two or more linear equations with the same variables, which must be solved together to find the common solution(s).

Graphing:

The process of representing equations or functions visually on a coordinate plane, allowing for the identification of the intersection point(s).

Substitution:

A method of solving a system of equations by isolating a variable in one equation and substituting it into the other equation to find the solution.