How Do You Solve a System of Equations Using the Elimination by Subtraction Method?

How Do You Solve a System of Equations Using the Elimination by Subtraction Method?

Note:

There are many different ways to solve a system of linear equations. In this tutorial, you'll see how to solve such a system by combining the equations together in a way so that one of the variables is eliminated. Then, see how find the value of that variable and use it to find the value of the other variable. Take a look!

Keywords:

  • problem
  • line
  • linear equations
  • system of equations
  • system
  • 2 equations
  • find intersection
  • solve system of equations
  • solve by elimination
  • elimination
  • variable elimination
  • subtract equations
  • consistent
  • 1 solution
  • independent
  • 2 equations
  • 2 unknowns
  • 2 variables

Background Tutorials

  • Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

      • What is a Variable?What is a Variable?

      What is a Variable?

      You can't do algebra without working with variables, but variables can be confusing. If you've ever wondered what variables are, then this tutorial is for you!

  • Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

      • How Do You Solve a System of Equations by Graphing?How Do You Solve a System of Equations by Graphing?

      How Do You Solve a System of Equations by Graphing?

      There are many different ways to solve a system of linear equations. In this tutorial, you'll see how to solve a system of linear equations by graphing both lines and finding their intersection. Take a look!

      • What's a System of Linear Equations?What's a System of Linear Equations?

      What's a System of Linear Equations?

      A system of equations is a set of equations with the same variables. If the equations are all linear, then you have a system of linear equations! To solve a system of equations, you need to figure out the variable values that solve all the equations involved. This tutorial will introduce you to these systems.

      • What's a Solution to a System of Linear Equations?What's a Solution to a System of Linear Equations?

      What's a Solution to a System of Linear Equations?

      If you have a system of equations that contains two equations with the same two unknown variables, then the solution to that system is the ordered pair that makes both equations true at the same time. Follow along as this tutorial uses an example to explain the sol

  • Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

      • How Do You Solve a System of Equations Using the Elimination by Addition Method?How Do You Solve a System of Equations Using the Elimination by Addition Method?

      How Do You Solve a System of Equations Using the Elimination by Addition Method?

      There are many different ways to solve a system of linear equations. In this tutorial, you'll see how to solve a system of linear equations by combining the equations together to eliminate one of the variables. Then, see how find the value of that variable and use it to find the value of the other variable. Take a look!

      • How Do You Solve Two Equations with Two Variables?How Do You Solve Two Equations with Two Variables?

      How Do You Solve Two Equations with Two Variables?

      Trying to solve two equations each with the same two unknown variables? Take one of the equations and solve it for one of the variables. Then plug that into the other equation and solve for the variable. Plug that value into either equation to get the value for the other variable. This tutorial will take you through this process of substitution step-by-step!

Further Exploration

  • Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

      • How Do You Solve a System of Equations Using the Elimination by Addition Method?How Do You Solve a System of Equations Using the Elimination by Addition Method?

      How Do You Solve a System of Equations Using the Elimination by Addition Method?

      There are many different ways to solve a system of linear equations. In this tutorial, you'll see how to solve a system of linear equations by combining the equations together to eliminate one of the variables. Then, see how find the value of that variable and use it to find the value of the other variable. Take a look!

  • Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.