How to Solve Systems of Equations Using Cramer's Rule

TL;DR

Cramer's rule allows you to solve systems of equations with two or three variables using determinants. For two variables, calculate the main determinant and two additional ones for x and y. For three variables, repeat the process to find the determinants for x, y, and z, using the appropriate coefficients and constants.

Transcript

now in this video we're going to go over kramer's rule and we're going to apply it to solve system of equations with two variables and three variables so let's start with a two variable system so let's say if we have the two equations a one x plus b one y let's say that's equal to c one and also a two x plus b2y is equal to c2 so to calculate the v... Read More

Key Insights

• 📏 Kramer's rule can be used to solve systems of equations with two and three variables.
• 🐞 Determinants are used to calculate the values of d, dx, dy, and dz.
• 🐞 The determinant d represents the main determinant of the system, while dx, dy, and dz represent the determinants of matrices obtained by replacing the coefficients with constants.

Questions & Answers

Q: What is Kramer's rule used for?

Kramer's rule is used to solve systems of equations with two and three variables.

Q: How do you calculate dx and dy using Kramer's rule for a two-variable system?

To calculate dx, replace the coefficients of x with the constants on the right side of the equations, and use the determinant formula. Similarly, for dy, replace the coefficients of y with the constants.

Q: How do you calculate dz using Kramer's rule for a three-variable system?

To calculate dz, replace the coefficients of z with the constants, using the same determinant formula as in the two-variable system.

Q: How do you use determinants to solve systems of equations with Kramer's rule?

Determinants are used to find the values of d, dx, dy, and dz in Kramer's rule, which are then used to calculate the values of x, y, and z.

Summary & Key Takeaways

• Kramer's rule can be used to solve systems of equations with two variables and three variables.

• To calculate the values of x and y in a two-variable system, use determinants and the rule of finding dx and dy.

• For three-variable systems, use determinants and the rule of finding dx, dy, and dz to solve for the values of x, y, and z.