Solving Systems of Equations Using the Substitution Method
Solve systems of linear equations in Grade 10 using substitution: isolate one variable in one equation, substitute into the other, and solve for both unknowns.
Key Concepts
New Concept The substitution method is a method used to solve systems of equations by solving an equation for one variable and substituting the resulting expression into the other equation.
Why it matters The substitution method is your first major tool for finding the exact intersection of two relationships, proving more powerful than simple graphing. Mastering this technique of replacement is crucial for solving more complex systems you'll encounter in science, engineering, and economics.
What’s next Next, you'll apply this method to solve for specific coordinate solutions and learn to recognize systems with no solution or infinite solutions.
Common Questions
What are the steps for solving by substitution?
Step 1: Isolate one variable in one equation. Step 2: Substitute that expression into the other equation. Step 3: Solve the resulting single-variable equation. Step 4: Back-substitute to find the other variable.
How do you solve x+y=5 and y=2x-1 by substitution?
Substitute y=2x-1 into x+y=5: x+(2x-1)=5, so 3x=6, x=2. Then y=2(2)-1=3. Solution: (2,3).
When does a substitution lead to a contradictory or identity equation?
If you get a false statement like 0=5, the system is inconsistent (no solution). If you get an identity like 0=0, the system is dependent (infinitely many solutions).