Solve a system of equations using substitution

Learning Objectives Isolate a variable in one of two linear equations. Substitute an algebraic expression into another equation to eliminate a variable. Solve the resulting single-variable equation to find the value of one variable. Back-substitute the found value to determine the value of the second variable. Identify if a system has one solution, no solution, or infinitely many solutions based on the algebraic outcome. Verify their solution by checking it in both original equations. Set up and solve a simple word problem by creating a system of equations and using substitution. Ever compared two different phone plans to see which is cheaper for your data usage? 📱 You were mentally setting up a system of equations to find the break-even point! This tutorial will teach y...

TermDefinitionExample System of EquationsA set of two or more equations that share the same variables. The goal is to find values for the variables that make all equations in the set true simultaneously.The set of equations y = 2x + 1 and 3x + 2y = 16 form a system. The solution is the specific (x, y) pair that works for both. Substitution MethodAn algebraic method for solving a system of equations by solving one equation for a variable and then substituting that expression into the other equation.In the system y = x + 3 and 2x + y = 9, we can substitute 'x + 3' for 'y' in the second equation to get 2x + (x + 3) = 9. Solution to a SystemAn ordered pair (x, y) or set of values that satisfies every equation in the system. Geometrically, it is the point of intersection of...

The Substitution Principle If a = b, then 'a' can be replaced by 'b' in any mathematical expression or equation. This is the fundamental principle behind the method. We isolate a variable in one equation (e.g., y = 3x + 4) to find an equivalent expression, then substitute that expression for the variable in the other equation. The Substitution Method Steps 1. Isolate a variable. 2. Substitute. 3. Solve. 4. Back-substitute. This is the four-step process for solving any system using substitution. First, solve one equation for one variable. Second, substitute the resulting expression into the other equation. Third, solve the new equation for the remaining variable. Fourth, plug the value you found back into one of the original equations to find the other var...