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- https://math.libretexts.org/Courses/Western_Connecticut_State_University/Draft_Custom_Version_MAT_131_College_Algebra/07%3A_Systems_of_Equations_and_Inequalities/7.01%3A_Systems_of_Linear_Equations_-_Two_VariablesA system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear ...A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. Systems of equations are classified as independent with one solution, dependent with an infinite number of solutions, or inconsistent with no solution.
- https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/03%3A_Solving_Linear_Systems/3.02%3A_Solving_Linear_Systems_with_Two_VariablesIn this section, we review a completely algebraic technique for solving systems, the substitution method11. The idea is to solve one equation for one of the variables and substitute the result into th...In this section, we review a completely algebraic technique for solving systems, the substitution method11. The idea is to solve one equation for one of the variables and substitute the result into the other equation. After performing this substitution step, we are left with a single equation with one variable, which can be solved using algebra.
- https://math.libretexts.org/Courses/Reedley_College/College_Algebra_1e_(OpenStax)/07%3A_Systems_of_Equations_and_Inequalities/7.01%3A_Systems_of_Linear_Equations_-_Two_VariablesA system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear ...A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. Systems of equations are classified as independent with one solution, dependent with an infinite number of solutions, or inconsistent with no solution.
- https://math.libretexts.org/Courses/Mission_College/Math_1%3A_College_Algebra_(Carr)/06%3A_Systems_of_Equations_and_Inequalities/6.02%3A_Systems_of_Linear_Equations_-_Two_VariablesA system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear ...A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. Systems of equations are classified as independent with one solution, dependent with an infinite number of solutions, or inconsistent with no solution.
- https://math.libretexts.org/Bookshelves/Algebra/Algebra_and_Trigonometry_1e_(OpenStax)/11%3A_Systems_of_Equations_and_Inequalities/11.01%3A_Systems_of_Linear_Equations_-_Two_VariablesA system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear ...A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. Systems of equations are classified as independent with one solution, dependent with an infinite number of solutions, or inconsistent with no solution.
- https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Arithmetic_and_Algebra_(ElHitti_Bonanome_Carley_Tradler_and_Zhou)/01%3A_Chapters/1.29%3A_Solving_a_System_of_Equations_AlgebraicallyHence, we get \(x=6 .\) To find \(y,\) we substitute \(x=6\) into the first equation of the system and solve for \(y\) (Note: We may substitute \(x=6\) into either of the two original equations or the...Hence, we get \(x=6 .\) To find \(y,\) we substitute \(x=6\) into the first equation of the system and solve for \(y\) (Note: We may substitute \(x=6\) into either of the two original equations or the equation \(y=7-x\) ): Hence \(x=10 .\) Now substituting \(x=10\) into the equation \(y=-3 x+36\) yields \(y=6,\) so the solution to the system of equations is \(x=10, y=6 .\) The final step is left for the reader.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_333%3A_Introduction_to_College_Algebra/07%3A_Systems_of_Equations_and_Inequalities/7.01%3A_Systems_of_Linear_Equations_-_Two_VariablesA system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear ...A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. Systems of equations are classified as independent with one solution, dependent with an infinite number of solutions, or inconsistent with no solution.
- https://math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_for_Science_Technology_Engineering_and_Mathematics_(Diaz)/04%3A_Systems_of_Linear_Equations_in_Two_and_Three_Variables/4.02%3A_Systems_of_Equations_-_The_Substitution_MethodSolving a system by graphing has its limitations. We rarely use graphing to solve systems. Instead, we use an algebraic approach. There are two approaches and the first approach is called substitution...Solving a system by graphing has its limitations. We rarely use graphing to solve systems. Instead, we use an algebraic approach. There are two approaches and the first approach is called substitution. We build the concepts of substitution through several examples and then conclude with a general four-step process to solve problems using this method.
- https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_(Arnold)/04%3A_Systems_of_Linear_Equations/4.02%3A_Solving_Systems_by_SubstitutionIn this section we introduce an algebraic technique for solving systems of two equations in two unknowns called the substitution method. The substitution method is fairly straightforward to use. First...In this section we introduce an algebraic technique for solving systems of two equations in two unknowns called the substitution method. The substitution method is fairly straightforward to use. First, you solve either equation for either variable, then substitute the result into the other equation. The result is an equation in a single variable. Solve that equation, then substitute the result into any of the other equations to find the remaining unknown variable.
- https://math.libretexts.org/Workbench/Algebra_and_Trigonometry_2e_(OpenStax)/11%3A_Systems_of_Equations_and_Inequalities/11.02%3A_Systems_of_Linear_Equations_-_Two_VariablesA system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear ...A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. Systems of equations are classified as independent with one solution, dependent with an infinite number of solutions, or inconsistent with no solution.
- https://math.libretexts.org/Courses/Los_Angeles_City_College/Math_245%3A_College_Algebra/07%3A_Systems_of_Equations_and_Inequalities/7.02%3A_Systems_of_Linear_Equations_-_Two_VariablesA system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear ...A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. Systems of equations are classified as independent with one solution, dependent with an infinite number of solutions, or inconsistent with no solution.
