📝 Practice Worksheets
🛠️ Related Tool
Systems of Linear Equations Explorer🔑 Key Concepts
- Use substitution when one equation already has a variable isolated or can be rewritten easily.
- Replace the isolated variable in the other equation with its equivalent expression.
- Substitution creates an equation containing only one variable.
- After finding one variable, substitute its value back into either original equation.
- Write the solution as an ordered pair \((x,y)\).
- The ordered pair represents the point where the two lines intersect.
- Check the solution in both original equations.
🧠 Math Vocabulary
- System of equations: Two or more equations containing the same variables.
- Substitution: Replacing a variable with an equivalent value or expression.
- Solution of a system: The ordered pair that makes both equations true.
- Ordered pair: A solution written as \((x,y)\).
- Intersection: The point where the graphs of two equations meet.
- Isolate: Rewrite an equation so one variable is alone on one side.
💡 Main Idea
To solve a system using substitution, isolate one variable and replace that variable in the other equation with its equivalent expression. Solve the resulting one-variable equation, substitute back to find the second variable, and write the solution as the ordered pair where the two lines intersect.
📚 What You Should Already Know
Students should know how to solve multi-step equations, distribute multiplication, combine like terms, perform integer operations, isolate variables, and substitute values or expressions into equations.
🚀 What Comes Next
Students will compare substitution with elimination and graphing, identify systems with no solution or infinitely many solutions, and apply systems of equations to real-world situations.
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