**One Step Equations Worksheet** – In math, **one step equations** or linear equations are a bunch of two or more linear equations that have several same sets of variables. The purpose of the system of linear equations (SPL) is to find the coordinate value.

To find the meeting value of two linear equations, you can use the substitution method and the elimination method. If a system of linear equations is depicted in a Cartesian diagram, the value of the system of linear equations is the meeting of the two linear equation lines.

There are several methods to solve the linear equation in order to obtain the value of the solution set, namely the graph method, the elimination method with equations, the elimination method by substitution, and the elimination method by adding or subtracting. Each method has its advantages and disadvantages.

**Solving One Step Equations Worksheet with Graphic and Elimination Methods**

### 1. Graphic Method

The one popular method of **one step equations** is determining the intersection point between two line of equations so that the set of solutions for the linear equation of the two variables is obtained. If the equation of the two lines is parallel to each other, then the set of solutions is the empty set.

Meanwhile, if the lines coincide with each other, the number of sets of solutions is infinite. The completion steps using the graphical method are as follows.

- Graph the lines ax + by = p and cx + dy = q in a Cartesian coordinate system. In this step, we must determine the intersection point of the X axis and the intersection of the Y axis, namely the intersection of the X axis when y = 0 and the intersection of the Y axis when x = 0. Then then the relationship between the two interceptions is to obtain an equation line.
- Determine the coordinates of the intersection of the two lines ax + by = p and cx + dy = q (if any).
- Write the set of solutions!

**Example:**

2x – y = 2

x + y = 4

**Answer:**

The intersection of the two lines obtained is (2,2). So, the set of solutions for the system of equations is (2,2). The advantage of the graphing method is that we can determine the set of solutions visually. This means that the results can be seen directly at a glance.

- Elimination Method

Suppose we have the **one step equations** in the variables x and y. This method requires you to eliminate one of the variables, x or y. An example is to find the x value of the two given equations.

As if the value of y is considered a known number, it is said that x is expressed in terms of y. Then the results obtained are equalized. Vice versa, the value of y can be expressed in terms of x, then we equate it from the equations.

Example:

3x + 5y = 21

2x – 7y = 45

Answer:

So, the set of solutions is {12, -3}. The disadvantage of the elimination method is that it takes too long a step because we have to eliminate these variables one by one. The longer the steps for solving it, the greater the chance for inaccuracy.

**Solving One-Step Equations with Elimination – Substitution Methods**

This **one step equations** method is a combination of the elimination and substitution method. First, choose one of the simple equations, then express y in x or x in y. Substitute the x or y obtained in step 1 into the other equation. Finally, solve the equation obtained in step 2.

Example:

3x + 2y = 10

9x – 7y = 43

Answer:

Step 1: Turn the equation into y variable.

Step 2: Find the value of x and y.

Step 3: Substitute the value of x and y into the equations.

So, the set of solutions is {4, -1}. The advantage of this method is very easy to use and effective. The weakness is that it is not recommended if it is used for complex linear equation problems such as a system of 3-variable linear equations.

After learning this method, you can easily solve the **One Step Equations Worksheet** or linear equations. The most important thing is you have to be careful when making the equations before answering your One Step Equations Worksheet. If you got it wrong, then you will get the wrong **one step equations** solving too.