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     How to Determine If an Ordered Pair is a Solution to a System of Equations

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     How to Determine If an Ordered Pair is a Solution to a System of Equations

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     Ordered pair solutions to equations | Graphing lines and slope | Algebra Basics | Khan Academy

     Nov 21, 2011

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   How do you determine if an ordered pair is a solution?

   • Substitute the ordered pair into each equation in the system. Determine whether true statements result from the substitution in both equations; if so, the ordered pair is a solution. \begin {array} {r}2x-y=-4\\ x-y=-1\end {array} 2x −y = −4 x −y = −1. They cross at what appears to be \left (-3,-2\right) (−3,−2).

   Study Guide - Ordered Pairs as Solutions to Systems - Symbolab

   www.symbolab.com/study-guides/cpcc-algebra-trig-l-/read-ordered-pairs-as-solutions-to-systems.html

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   How do you solve a equation with an ordered pair?

   • Write the solution as an ordered pair. Check that the ordered pair is a solution to both original equations. Now we’ll do an example where we need to multiply both equations by constants in order to make the coefficients of one variable opposites. Solve the system by elimination: {4x − 3y = 9 7x + 2y = − 6

   4.2: Solve Systems of Linear Equations with Two Variables

   math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_1e_(OpenStax)/04:_Systems_of_Linear_Equations/4.02:_Solve_Systems_of_Linear_Equations_with_Two_Variables

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   Do all systems of linear equations have a single ordered pair?

   • When we solved the system by graphing, we saw that not all systems of linear equations have a single ordered pair as a solution. When the two equations were really the same line, there were infinitely many solutions. We called that a consistent system. When the two equations described parallel lines, there was no solution.

   4.2: Solve Systems of Linear Equations with Two Variables

   math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_1e_(OpenStax)/04:_Systems_of_Linear_Equations/4.02:_Solve_Systems_of_Linear_Equations_with_Two_Variables

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   What is a solution to a system of two linear equations?

   • A solution of a system of two linear equations is represented by an ordered pair (x, y). To determine if an ordered pair is a solution to a system of two equations, we substitute the values of the variables into each equation. If the ordered pair makes both equations true, it is a solution to the system.

   4.2: Solve Systems of Linear Equations with Two Variables

   math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_1e_(OpenStax)/04:_Systems_of_Linear_Equations/4.02:_Solve_Systems_of_Linear_Equations_with_Two_Variables

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   What is a solution of a system of equations?

   • The solutions of a system of equations are the values of the variables that make all the equations true. A solution of a system of two linear equations is represented by an ordered pair (x, y). To determine if an ordered pair is a solution to a system of two equations, we substitute the values of the variables into each equation.

   4.2: Solve Systems of Linear Equations with Two Variables

   math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_1e_(OpenStax)/04:_Systems_of_Linear_Equations/4.02:_Solve_Systems_of_Linear_Equations_with_Two_Variables

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   Which pair satisfies both equations?

   • The ordered pair \left (5,1\right) (5,1) satisfies both equations, so it is the solution to the system. We can see the solution clearly by plotting the graph of each equation. Since the solution is an ordered pair that satisfies both equations, it is a point on both of the lines and thus the point of intersection of the two lines.

   Study Guide - Ordered Pairs as Solutions to Systems - Symbolab

   www.symbolab.com/study-guides/cpcc-algebra-trig-l-/read-ordered-pairs-as-solutions-to-systems.html

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3. www.youtube.com › watchHow to Determine If an Ordered Pair is a Solution to a System ...

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   This algebra video tutorial explains how to determine if an ordered pair is a solution to a system of equations. Access Full-Length Premium Videos: ...

   • Video Duration: 3 min
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   • Author: The Organic Chemistry Tutor

4. www.symbolab.com › study-guides › cpcc-algebra-trigStudy Guide - Ordered Pairs as Solutions to Systems - Symbolab

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   How To: Given a system of linear equations and an ordered pair, determine whether the ordered pair is a solution. Substitute the ordered pair into each equation in the system. Determine whether true statements result from the substitution in both equations; if so, the ordered pair is a solution.

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6. www.youtube.com › watchHow to Determine If an Ordered Pair is a Solution ... - YouTube

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   This algebra math tutorial explains how to determine whether an ordered pair is a solution to a system of linear equations. To determine if an ordered pair i...

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   Jul 19, 2023 · 483K subscribers. Subscribed. 14. 1.2K views 1 year ago. In this video I show you how to determine if an ordered pair is a solution to a systems of equations. Slope Intercept Form...

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8. math.libretexts.org › Bookshelves › Algebra4.2: Solve Systems of Linear Equations with Two Variables

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   Feb 14, 2022 · A solution of a system of two linear equations is represented by an ordered pair (x, y). To determine if an ordered pair is a solution to a system of two equations, we substitute the values of the variables into each equation. If the ordered pair makes both equations true, it is a solution to the system.

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

   math.libretexts.org › Bookshelves › Algebra

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   May 2, 2022 · Given a system of linear equations and an ordered pair, determine whether the ordered pair is a solution. Substitute the ordered pair into each equation in the system. Determine whether true statements result from the substitution in both equations; if so, the ordered pair is a solution.

10. pressbooks.bccampus.ca › algebraintermediateSolve Systems of Linear Equations with Two Variables

    pressbooks.bccampus.ca › algebraintermediate

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    A solution of a system of two linear equations is represented by an ordered pair. To determine if an ordered pair is a solution to a system of two equations, we substitute the values of the variables into each equation. If the ordered pair makes both equations true, it is a solution to the system.