Solve a system of equations using elimination word problems

Learning Objectives Translate a word problem into a system of two linear equations with two variables. Identify when the elimination method is an efficient strategy for solving a system of equations. Modify one or both linear equations by multiplication to create opposite coefficients for one variable. Apply the elimination method to solve for one variable, and then use substitution to solve for the second. Interpret the numerical solution in the context of the original word problem. Verify their solution by checking it against the conditions described in the word problem. Ever wonder how a concert venue knows exactly how many adult and child tickets were sold if they only know the total attendance and total revenue? 🎟️ Let's use algebra to uncover the secrets! This tu...

TermDefinitionExample System of Linear EquationsA set of two or more linear equations that share the same variables. The solution to the system is the point (or set of points) that satisfies all equations simultaneously.The equations `x + y = 10` and `2x - y = 8` form a system. The solution is the specific pair of `x` and `y` values that makes both equations true. VariableA symbol, usually a letter, that represents an unknown quantity in a mathematical expression or equation.In a problem about the cost of apples and bananas, we might use `a` to represent the cost of one apple and `b` for the cost of one banana. CoefficientThe numerical factor that is multiplied by a variable.In the term `7d`, which could represent the value of `d` dimes, the coefficient is 7. Elimination MethodA method fo...

Standard Form of a Linear Equation Ax + By = C This form is ideal for the elimination method. When you write word problems as equations, arranging them in this standard form aligns the variables and constants vertically, making it easy to add or subtract the equations. Addition Property of Equality If a = b and c = d, then a + c = b + d This is the core principle behind elimination. It allows us to add the left sides of two equations and the right sides of two equations to create a new, valid equation. We do this strategically to eliminate a variable. Multiplication Property of Equality If a = b, then ac = bc (where c ≠ 0) This property lets us multiply an entire equation by a non-zero constant to create an equivalent equation. We use this to create opposite coeffici...