Sure. Here is a simple example of how to solve a system of equations using Gaussian elimination:

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Given the system of equations:

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x + y = 2

x - y = 0
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We can solve this system using Gaussian elimination as follows:

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1. Add the first equation to the second equation.

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2. x + 0 = 2

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3. x = 2

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4. Substitute x = 2 into the first equation to solve for y.

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2 + y = 2

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5. y = 0

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Therefore, the solution to the system of equations is x = 2, y = 0.
Here is a simple example of how to solve a system of equations using Cramer's rule:

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Given the system of equations:

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x + y = 2

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x - y = 0
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We can solve this system using Cramer's rule as follows:

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1. Calculate the determinant of the coefficient matrix.

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| 1 1 | = 1
| 1 -1 |

Calculate the determinant of the matrix formed by replacing the first column with the constants on the right-hand side of the equations.
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| 2 1 | = 2
| 0 -1 |

Calculate the determinant of the matrix formed by replacing the second column with the constants on the right-hand side of the equations.
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| 1 2 | = 2
| 1 0 |

Divide the determinant of the matrix formed by replacing the first column with the constants on the right-hand side of the equations by the determinant of the coefficient matrix.
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x = 2/1 = 2

Divide the determinant of the matrix formed by replacing the second column with the constants on the right-hand side of the equations by the determinant of the coefficient matrix.
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y = 2/1 = 2

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Therefore, the solution to the system of equations is x = 2, y = 2.
As you can see, Gaussian elimination is a more efficient way to solve systems of equations than Cramer's rule. Gaussian elimination can be used to solve systems of equations with any number of equations, while Cramer's rule is only efficient for systems of equations with a small number of equations.