Solve a system of equations using elimination: word problems

Learning Objectives Translate real-world word problems into a system of two linear equations. Identify coefficients that can be eliminated or made into additive inverses. Apply the elimination method to solve a system of linear equations. Find the values of both variables in a system of equations. Interpret the solution of a system of equations in the context of the original word problem. Check their solutions by substituting values back into the original equations. Ever wondered how stores figure out the price of individual items when they only tell you the total for a bundle? 🛍️ Systems of equations can help us solve these everyday mysteries! In this lesson, you'll learn how to take real-world situations described in words and turn them into mathematical equations. W...

TermDefinitionExample System of Linear EquationsTwo or more linear equations that share the same variables. The solution to a system is the point (or values for the variables) that satisfies all equations simultaneously.Equation 1: $x + y = 10$ Equation 2: $2x - y = 5$ VariableA symbol, usually a letter, that represents an unknown quantity or value in an equation.In the equation $2x + 3y = 7$, 'x' and 'y' are variables representing unknown numbers. CoefficientA numerical factor multiplied by a variable in an algebraic term.In the term $5x$, '5' is the coefficient. In $y$, the coefficient is '1'. Elimination MethodA technique for solving systems of linear equations by adding or subtracting the equations to eliminate one of the variables, allowing you...

Standard Form of a Linear Equation $Ax + By = C$ This is a common way to write linear equations, where A, B, and C are constants, and x and y are variables. When setting up systems for elimination, it's often helpful to arrange both equations in this form. Additive Inverse Property $a + (-a) = 0$ This property is fundamental to the elimination method. We manipulate equations so that the coefficients of one variable become additive inverses, allowing that variable to cancel out when the equations are added. Steps for the Elimination Method 1. Align equations in standard form. 2. Multiply one or both equations by a constant to create additive inverse coefficients for one variable. 3. Add or subtract the equations to eliminate one variable. 4. Solve for the remaining...