Solving Systems by Substitution Method
Solving systems of equations by the substitution method is a Grade 7 algebra skill in Big Ideas Math Advanced 2, Chapter 5: Systems of Linear Equations. The method involves solving one equation for a variable, substituting that expression into the other equation to reduce it to a single variable, then solving and back-substituting. The substitution method is most efficient when one variable already has a coefficient of 1 or negative 1.
Key Concepts
A solution to a $2 \times 2$ linear system is an ordered pair that satisfies both equations.
The substitution method involves solving one equation for a variable, then substituting that expression into the other equation.
Common Questions
How do you solve a system of equations using substitution?
Step 1: Solve one equation for a variable. Step 2: Substitute that expression into the other equation. Step 3: Solve the resulting single-variable equation. Step 4: Substitute back to find the other variable.
When should you use the substitution method?
Use substitution when one equation is already solved for a variable, or when one variable has a coefficient of 1 or negative 1, making it easy to isolate without creating fractions.
What is the solution to a system of equations?
The solution is an ordered pair (x, y) that satisfies both equations simultaneously. Graphically, it represents the point where the two lines intersect.
What textbook covers solving systems by substitution in Grade 7?
Big Ideas Math Advanced 2, Chapter 5: Systems of Linear Equations covers the substitution method for solving 2-variable linear systems.