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      • The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. In this example, the ordered pair (4, 7) is the solution to the system of linear equations. We can verify the solution by substituting the values into each equation to see if the ordered pair satisfies both equations.

      11.1: Systems of Linear Equations - Two Variables ...

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  3. math.libretexts.org › Bookshelves › Algebra11.1: Systems of Linear Equations - Two Variables ...

    The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. In this example, the ordered pair \((4,7)\) is the solution to the system of linear equations. We can verify the solution by substituting the values into each equation to see if the ordered pair satisfies both equations.

  4. openstax.org › books › college-algebra-2e7.1 Systems of Linear Equations: Two Variables - OpenStax

    • Determining Whether an Ordered Pair Is a Solution to a System of Equations. Determine whether the ordered pair ( 5,1 ) ( 5,1 ) is a solution to the given system of equations.
    • Solving a System of Equations in Two Variables by Graphing. Solve the following system of equations by graphing. Identify the type of system. 2x+y=−8 x−y=−1 2x+y=−8 x−y=−1.
    • Solving a System of Equations in Two Variables by Substitution. Solve the following system of equations by substitution. −x+y=−5 2x−5y=1 −x+y=−5 2x−5y=1.
    • Solving a System by the Addition Method. Solve the given system of equations by addition. x+2y=−1 −x+y=3 x+2y=−1 −x+y=3. Solution. Both equations are already set equal to a constant.

  5. openstax.org › books › intermediate-algebra-2e4.1 Solve Systems of Linear Equations with Two Variables

    • Determine whether the ordered pair is a solution to the system {3x+y=0x+2y=−5. {3x+y=0x+2y=−5. ⓐ (1,−3)(1,−3) ⓑ (0,0)(0,0)
    • Determine whether the ordered pair is a solution to the system {x−3y=−8−3x−y=4. {x−3y=−8−3x−y=4. ⓐ (2,−2)(2,−2) ⓑ (−2,2)(−2,2)
    • Solve the system by graphing: {x−3y=−3x+y=5. {x−3y=−3x+y=5.
    • Solve the system by graphing: {−x+y=13x+2y=12. {−x+y=13x+2y=12. The steps to use to solve a system of linear equations by graphing are shown here.

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  7. www.symbolab.com › study-guides › precalctwoStudy Guide - Systems of Linear Equations: Two Variables

    The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. In this example, the ordered pair (4, 7) is the solution to the system of linear equations.

  8. www.symbolab.com › study-guides › boundless-algebraStudy Guide - Systems of Equations in Two Variables - Symbolab

    The solution to a system of linear equations in two variables is any ordered pair [latex](x, y)[/latex] that satisfies each equation independently. Graphically, solutions are points at which the lines intersect. Key Terms. system of linear equations: A set of two or more equations made up of two or more variables that are considered simultaneously.

  9. math.libretexts.org › Bookshelves › Applied5.10: Systems of Linear Equations in Two Variables

    To solve a system of two linear equations, we want to find the values of the variables that are solutions to both equations. In other words, we are looking for the ordered pairs ( x x , y y ) that make both equations true.

  10. courses.lumenlearning.com › wmopen-collegealgebraSystems of Linear Equations: Two Variables | College Algebra

    The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. In this example, the ordered pair (4, 7) is the solution to the system of linear equations. We can verify the solution by substituting the values into each equation to see if the ordered pair satisfies both equations.