What is the cake method?

The "cake method" is a term often used to describe a method for solving systems of linear equations, specifically when there are two variables. While it's not a formal mathematical term, it's a helpful mnemonic for students to remember the steps involved.

Here's how the "cake method" works:

1. The "Cake" Setup

* Line 1: Write the first equation in the system.

* Line 2: Write the second equation directly below the first.

* Line 3: This is for the "icing" - it's where you'll write the result of combining the equations.

2. "Mixing" the Equations

* Choose a variable to eliminate. Look for coefficients that are either the same or opposites.

* Multiply one or both equations by a constant to make the coefficients of the chosen variable match. This could involve multiplying one equation by -1 to make the coefficients opposite.

* Add the equations together. This will eliminate one variable.

3. "Baking" the Solution

* Solve for the remaining variable.

* Substitute the value of this variable back into either of the original equations.

* Solve for the other variable.

Example:

Solve the system of equations:

* 2x + 3y = 7

* x - 2y = 4

Cake Method Steps:

1. Cake Setup:

* 2x + 3y = 7

* x - 2y = 4

* _____________

2. Mixing:

* Multiply the second equation by -2: -2x + 4y = -8

* Add the modified second equation to the first equation:

2x + 3y = 7

-2x + 4y = -8

_______________

7y = -1

3. Baking:

* Solve for y: y = -1/7

* Substitute y = -1/7 into either original equation. Let's use the first:

2x + 3(-1/7) = 7

2x - 3/7 = 7

2x = 52/7

x = 26/7

* The solution is (x, y) = (26/7, -1/7)

Important Note: The "cake method" is just a way to remember the steps involved in solving a system of equations. It doesn't change the underlying mathematical concepts.

There are other methods for solving systems of equations, such as substitution and matrix methods, which may be more efficient for larger systems.