# System Linear Equations Worksheet Elise Austin - March 10, 2022 - Math Worksheet

In human daily life, consciously or unconsciously system, linear equations are used in various activities. One of them is for cost budgeting activities. The system of linear equations itself is an algebraic equation. Algebra is a branch of mathematics that uses certain symbols and letters to represent the value of a material.

Linear equations are one of the systems found in mathematics. This system is included in algebra, which is a branch of mathematics that uses signs and letters to represent certain numbers.

The system of linear equations can be used by humans in everyday life. For example, in terms of budgeting usage costs and operating costs of a company.

To understand this system further, consider the following explanation of the system of linear equations.

## System of Linear Equations

The system of linear equations is one of the algebraic equations. This equation has the characteristic that each term contains a constant or the product of a constant with a single variable.

This equation is said to be linear because this mathematical relationship can be described as a straight line in the Cartesian coordinate system, a system that assigns each point uniquely in a plane to a series of numerical coordinates.

This system of linear equations generally has two main properties, namely:

The addition and subtraction of numbers on both sides of equation l, does not change the solution of the equation.
Multiplying a non-zero number on both sides of equation l, does not change the solution of the equation.

Linear equations are grouped into 3 types based on the number of variables. The types of systems of linear equations, namely:

### 1. One Variable Linear Equation

The general form of this type of equation is ax + b = 0, provided that a 0 and b = constant
Solution: x = – b/a.

For example, 5x + 10 then x = – 10/5, so the value of the letter x is -2.

### 2. Linear Equation of Two Variables

The general form of this type of equation is ax + by = c, provided that a, b, c are constants.

The solution can use the elimination method, which is the method of eliminating or eliminating the value of a variable, and the substitution method, which is replacing the value of a variable in one equation from another equation.

### 3. Linear Equation of Three Variables

The general form of this equation is ax + by + cz = d, where a, b, c, d are constants. Solving linear equations of three variables can use the method of solving equations of two variables, namely the elimination method as described previously.

Linear equations of three variables can also be solved by substitution, integration, and determination methods. The following is an example of a home school math worksheet linear equations exercise.

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