These worksheets teach your students to apply algebraic solutions to linear equations to identify variables.

When we have a set of two or more linear equations, we refer to this a system. We are constantly missing two variables in these systems denoted by x and y. The goal is to find a similarity between them. This can be done by committing to a single variable, either substitute x for y or vice versa. Once you plug in their values, everything will come to light.

A group of equations that you can solve collectively is called system of equations. When we have two linear equations with two variables, it means we are making fundamental linear system. If we talk about graph plotting, we represent such equations on straight lines. We use simultaneous equations for the system of equations. Here, simultaneous means being solved that is at the same time. In algebra, we have two basic ways of solving linear equation or systems. The one is substitution method and the other one is elimination method that is addition or subtraction method. Substitution Method - In this method, we replace two variables in a linear system with an equivalent expression. We can achieve this goal by plugging it into the other equation and solving one variable from one equation. Elimination Method - In this method, one group of variables cancel each other out while adding or subtracting equations. But there is another way that make cancellation possible that might be necessary. This method helps you to create coefficients for these variables that are the same or negatives. When you multiply via equations, it means you are near to your goal of creation process. These worksheets explain how to solve for variables by applying algebraic solutions to linear equations. Make sure to double check your work by checking the reverse to reach where you started.

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Algebraic Solutions to Linear Systems Worksheets

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Algebraic Solutions to Linear Equations Lesson and Practice

Students will practice solving for variables by applying algebraic solutions to linear equations. A sample problem is solved and two practice problems are provided.


Students will solve for variables using a series of ninja-like moves with algebra. Ten problems are provided.


Students will apply algebraic solutions to linear equations to solve for variables. Ten problems are provided.

Review and Practice

Subtract second equation from first. Find value of y. Insert the value of y in any of the equation and find the value of x.


Students demonstrate their proficiency of being able to solve for these variables. Ten problems are provided.

Skills Check

This is good to use as a review or a method to introduce or review the skills that we have learned on this topic. Three problems are provided, and space is included for students to copy the correct answer when given.