Solve the system of equations by combining the equations

Thomas D.

asked • 01/03/16

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1 Expert Answer

Michael J. answered • 01/03/16

Great at Simplifying Complex Concepts and Processes

3x + 4y = -32            eq1

3x + 5y = -43            eq2

Combining equations means that we either add or subtract the equations in order to eliminate an x term or y term.  We can subtract eq2 from eq1 to eliminate the x terms.

-y = 11

y = -11

Now substitute this value of y into eq1 to solve for x.  I'll let you complete this step on your own.

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Solve the system of equations by combining the equations
Real math help.

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

  • Systems of Equations

      • Solve the system of equations by combining the equations
        Solve the system of equations by combining the equations

      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!

  • Numerical and Algebraic Expressions

      • Solve the system of equations by combining the equations
        Solve the system of equations by combining the equations

      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!

  • Definitions of Linear Systems

      • Solve the system of equations by combining the equations
        Solve the system of equations by combining the 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.

      • Solve the system of equations by combining the equations
        Solve the system of equations by combining the 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 solution to a system of equations!

  • Solving Systems by Graphing

      • Solve the system of equations by combining the equations
        Solve the system of equations by combining the equations

      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!

  • Solving Systems Using Substitution

      • Solve the system of equations by combining the equations
        Solve the system of equations by combining the equations

      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

  • Systems of Equations

      • Solve the system of equations by combining the equations
        Solve the system of equations by combining the equations

      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!

      • Solve the system of equations by combining the equations
        Solve the system of equations by combining the equations

How do you solve systems of equations?

To solve a system of equations using substitution:.
Isolate one of the two variables in one of the equations..
Substitute the expression that is equal to the isolated variable from Step 1 into the other equation. ... .
Solve the linear equation for the remaining variable..

Why do we combine equations?

Combining equations is a powerful tool for solving a system of equations. Adding or subtracting two equations in order to eliminate a common variable is called the elimination method. Once one variable is eliminated, it becomes much easier to solve for the other one.

What are the 3 methods for solving systems of equations?

There are three ways to solve systems of linear equations in two variables: graphing. substitution method. elimination method.