Solve a system of equations using elimination

Learning Objectives Identify a system of two linear equations with two variables. Explain the goal of the elimination method in solving systems of equations. Multiply an entire equation by a constant to create opposite or identical coefficients for a variable. Add or subtract two equations to eliminate one variable. Solve the resulting one-variable equation. Substitute the value of one variable back into an original equation to find the other variable. Check their solution by substituting both values into both original equations. Imagine you have two clues to find two secret numbers! 🕵️‍♀️ How can you use both clues together to figure out what each number is? In this lesson, you'll learn a powerful method called 'elimination' to solve problems with two unkn...

TermDefinitionExample System of EquationsA set of two or more equations that share the same variables. We are looking for values for the variables that make ALL equations true at the same time.Equation 1: x + y = 10 Equation 2: x - y = 2 VariableA letter (like x or y) that represents an unknown number in an equation.In '2x + 3 = 7', 'x' is the variable. CoefficientThe number multiplied by a variable in an algebraic term.In '5x', '5' is the coefficient of 'x'. In 'y', '1' is the coefficient of 'y'. Elimination MethodA strategy to solve a system of equations by adding or subtracting the equations to 'eliminate' (make disappear) one of the variables.If you have 'x + y = 5' and 'x - y = 1&...

Rule 1: Multiplying an Equation To change the coefficients of a variable, you can multiply every term in an entire equation by the same non-zero number. If $A x + B y = C$, then $k(A x + B y) = kC$ becomes $k A x + k B y = k C$. Use this rule to make the coefficients of one variable either opposite (e.g., 2y and -2y) or identical (e.g., 3x and 3x) in both equations. Remember to multiply EVERY term on BOTH sides of the equation! Rule 2: Adding Equations to Eliminate If you have two equations where one variable has opposite coefficients, you can add the two equations together to eliminate that variable: $(A x + B y) + (D x - B y) = C + E$ simplifies to $(A+D)x = C+E$. This rule is used when you have terms like '+2y' and '-2y'. Adding them together results i...