Solve a system of equations using elimination: word problem

Learning Objectives Translate a complex word problem into a system of two linear equations with two variables. Identify when the elimination method is the most efficient strategy for solving a system derived from a word problem. Manipulate one or both equations by multiplication to create opposite coefficients for one variable. Apply the elimination method to solve for one variable in a real-world context. Substitute the found value back into an original equation to solve for the second variable. Interpret the solution (x, y) in the context of the original word problem and state the answer with appropriate units. How can an event planner determine the exact number of adult and child tickets sold if they only know the total revenue and total attendance? 🤔🎟️ This tutorial wi...

TermDefinitionExample System of Linear EquationsA set of two or more linear equations that share the same variables. The solution to the system is the ordered pair (x, y) that satisfies all equations simultaneously.The equations x + y = 10 and 2x - y = 8 form a system. The solution is (6, 4) because 6 + 4 = 10 and 2(6) - 4 = 8. Elimination MethodAn algebraic technique for solving a system of equations where one equation is added to or subtracted from the other to 'eliminate' one of the variables.For the system x + y = 5 and x - y = 1, adding the two equations results in 2x = 6, which eliminates 'y'. Variable RepresentationAssigning variables (like x and y) to represent the unknown quantities described in a word problem.In a problem about ticket sales, 'x' cou...

Standard Form for Elimination Ax + By = C Arrange both equations in this form before attempting elimination. This ensures that like terms are vertically aligned, making addition or subtraction straightforward. Multiplication Property of Equality If a = b, then ac = bc Used to multiply an entire equation by a non-zero constant. This is the key step to create opposite coefficients for one of the variables if they don't already exist. Addition Property of Equality If a = b and c = d, then a + c = b + d This is the core principle of elimination. We add the left sides of two equations and the right sides of two equations to create a new, valid equation with one variable eliminated.