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- https://math.libretexts.org/Courses/Los_Angeles_City_College/Math_230-Mathematics_for_Liberal_Arts_Students/01%3A_Linear_Equations/1.05%3A_More_ApplicationsIn a free market economy the supply curve for a commodity is the number of items of a product that can be made available at different prices, and the demand curve is the number of items the consumer w...In a free market economy the supply curve for a commodity is the number of items of a product that can be made available at different prices, and the demand curve is the number of items the consumer will buy at different prices. The supply curve for a product is \(y = 3.5x - 14\) and the demand curve for the same product is \(y = - 2.5x + 34\), where x is the price and y the number of items produced.
- 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/Bookshelves/Applied_Mathematics/Applied_Finite_Mathematics_(Sekhon_and_Bloom)/01%3A_Linear_Equations/1.05%3A_More_ApplicationsIn a free market economy the supply curve for a commodity is the number of items of a product that can be made available at different prices, and the demand curve is the number of items the consumer w...In a free market economy the supply curve for a commodity is the number of items of a product that can be made available at different prices, and the demand curve is the number of items the consumer will buy at different prices. The supply curve for a product is \(y = 3.5x - 14\) and the demand curve for the same product is \(y = - 2.5x + 34\), where x is the price and y the number of items produced.
- https://math.libretexts.org/Courses/Community_College_of_Denver/MAT_1320_Finite_Mathematics_2e/01%3A_Solving_Linear_Equations/1.04%3A_Solving_Systems_of_Linear_Equations_in_Two_VariablesA system of linear equations consists of two or more linear equations made up of two or more variables such that all equations in the system are considered simultaneously. Systems are helpful for us ...A system of linear equations consists of two or more linear equations made up of two or more variables such that all equations in the system are considered simultaneously. Systems are helpful for us to determine relationships between supply, demand, revenue, cost, and profit.
- https://math.libretexts.org/Courses/Irvine_Valley_College/Math_26%3A_Introduction_to_Linear_Algebra/01%3A_Systems_of_Linear_Equations/1.02%3A_Row_ReductionLearn how the elimination method corresponds to performing row operations on an augmented matrix. Vocabulary words: row operation, row equivalence, matrix, augmented matrix, pivot, (reduced) row echel...Learn how the elimination method corresponds to performing row operations on an augmented matrix. Vocabulary words: row operation, row equivalence, matrix, augmented matrix, pivot, (reduced) row echelon form, free variable Instead of relying on graphing (which can be hard in the \(xy\)-plane, and very hard in the \(xyz\)-space, and impossible for higher dimensions) or substitution, we begin with elimination and introduce matrices to help keep things organized.
- 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/4.03%3A_System_of_Equations_-_The_Addition_MethodThe substitution method is often used for solving systems in various areas of algebra. However, substitution can get quite involved, especially if there are fractions because this only allows more roo...The substitution method is often used for solving systems in various areas of algebra. However, substitution can get quite involved, especially if there are fractions because this only allows more room for error. Hence, we need an even more sophisticated way for solving systems in general. We call this method the addition method, also called the elimination method. We will build the concept in the following examples, then define a four-step process we can use to solve by elimination.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Introduction_to_Game_Theory%3A_A_Discovery_Approach_(Nordstrom)/03%3A_Repeated_Two-Person_Zero-sum_Games/3.06%3A_Augmented_MatricesIn this section, we will see how to use matrices to solve systems of equations. In both the graphical method and the expected value method, you have had to solve a system of equations.
- https://math.libretexts.org/Courses/University_of_St._Thomas/Math_101%3A_Finite_Mathematics/06%3A_Linear_Functions/6.04%3A_Intersection_of_Straight_LinesIn a free market economy the supply curve for a commodity is the number of items of a product that can be made available at different prices, and the demand curve is the number of items the consumer w...In a free market economy the supply curve for a commodity is the number of items of a product that can be made available at different prices, and the demand curve is the number of items the consumer will buy at different prices. The supply curve for a product is \(y = 3.5x - 14\) and the demand curve for the same product is \(y = - 2.5x + 34\), where x is the price and y the number of items produced.
- https://math.libretexts.org/Courses/Coalinga_College/Math_for_Educators_(MATH_010A_and_010B_CID120)/08%3A_Algebraic_Thinking/8.14%3A_System_of_Equations_-_The_Addition_MethodThe substitution method is often used for solving systems in various areas of algebra. However, substitution can get quite involved, especially if there are fractions because this only allows more roo...The substitution method is often used for solving systems in various areas of algebra. However, substitution can get quite involved, especially if there are fractions because this only allows more room for error. Hence, we need an even more sophisticated way for solving systems in general. We call this method the addition method, also called the elimination method. We will build the concept in the following examples, then define a four-step process we can use to solve by elimination.
- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/MAT_149%3A_Topics_in_Finite_Mathematics_(Holz)/03%3A_Systems_and_Matrices/3.01%3A_Systems_of_Linear_Equations/3.1.01%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/Under_Construction/Purgatory/MAT_1320_Finite_Mathematics/03%3A_Solving_Systems_of_Equations/3.01%3A_Solving_Systems_with_AlgebraA system of linear equations consists of two or more linear equations made up of two or more variables such that all equations in the system are considered simultaneously. Systems are helpful for us ...A system of linear equations consists of two or more linear equations made up of two or more variables such that all equations in the system are considered simultaneously. Systems are helpful for us to determine relationships between supply, demand, revenue, cost, and profit.
