Solving Systems of Equations Using the Elimination Method
Solve linear systems in Grade 10 using elimination: multiply equations to align coefficients, add or subtract to eliminate one variable, then back-substitute to find the solution.
Key Concepts
New Concept When the elimination method is used, the two equations are added. The sum of one of the variables is $0$.
What’s next Next, you’ll solve systems by adding equations, sometimes multiplying them by a constant to enable elimination.
Common Questions
What are the steps for the elimination method?
Multiply one or both equations by constants so that coefficients of one variable are opposites, then add the equations to eliminate that variable, solve for the remaining variable, and back-substitute.
How do you solve 2x+3y=12 and 4x-3y=6 by elimination?
The y-coefficients are already opposites (+3 and -3). Add both equations: 6x=18, so x=3. Substitute x=3 into first equation: 6+3y=12, y=2. Solution: (3,2).
How do you eliminate a variable when no coefficients are opposites?
Multiply one or both equations by appropriate constants. For 2x+y=5 and x+3y=10, multiply the second by -2 to get -2x-6y=-20, then add to eliminate x.