Solve a system of equations using substitution word problems

Learning Objectives Translate a real-world scenario into a system of two linear equations. Identify which variable is most efficient to isolate for substitution. Algebraically isolate a variable in a linear equation. Correctly substitute an algebraic expression into a second equation to create a single-variable equation. Solve for both variables in the system. Interpret the numerical solution in the context of the original word problem. Ever tried to figure out the cost of a single taco versus a burrito in a combo deal? 🌮🌯 Let's use algebra to solve real-world puzzles like this! This tutorial will guide you through the process of translating word problems into systems of linear equations. You will then master the substitution method, a powerful algebraic technique to...

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 `y = 2x + 1` and `3x + 2y = 16` form a system. The solution is the specific (x, y) pair that makes both statements true. VariableA symbol, typically a letter, used to represent an unknown numerical value in an equation.In a problem about ticket sales, we might use 'a' to represent the cost of an adult ticket and 'c' for the cost of a child's ticket. Isolating a VariableThe process of rearranging an equation so that one variable is by itself on one side of the equals sign.To isolate 'y' in the equation `4x + y = 10`, you woul...

The Substitution Principle If `a = b`, then `a` can be replaced by `b` in any mathematical statement. This is the foundational logic of the substitution method. Once we isolate a variable (e.g., `y = 3x - 4`), we have two equivalent expressions (`y` and `3x - 4`). We can then replace `y` with `3x - 4` in the other equation of the system. Ideal Form for Substitution y = mx + b \quad \text{or} \quad x = my + b When one of the equations in your system is already in slope-intercept form (or solved for x), it is perfectly set up for the substitution method. The expression `mx + b` can be directly substituted for the variable `y`.