Solving systems of equations by substitution is a key technique in algebra. It involves isolating a in one and plugging it into another, allowing you to solve for both variables step-by-step.
This method is particularly useful when one equation is already solved for a variable. It's often more efficient than other methods, especially with complex fractions or when one variable has a of 1 or -1.
Solving Systems of Equations by Substitution
Substitution method for linear systems
Top images from around the web for Substitution method for linear systems
OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials: Solving Linear Systems by Substitution View original
Is this image relevant?
OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials: Solving Linear Systems by Substitution View original
Is this image relevant?
OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials: Solving Linear Systems by Substitution View original
Is this image relevant?
OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials: Solving Linear Systems by Substitution View original
Is this image relevant?
OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials: Solving Linear Systems by Substitution View original
Is this image relevant?
1 of 3
Top images from around the web for Substitution method for linear systems
OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials: Solving Linear Systems by Substitution View original
Is this image relevant?
OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials: Solving Linear Systems by Substitution View original
Is this image relevant?
OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials: Solving Linear Systems by Substitution View original
Is this image relevant?
OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials: Solving Linear Systems by Substitution View original
Is this image relevant?
OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials: Solving Linear Systems by Substitution View original
Is this image relevant?
1 of 3
Involves solving one equation for one variable and substituting the resulting expression into the other equation
Isolate one variable in one of the equations (choose the equation and variable resulting in the simplest )
Substitute this expression for the variable into the other equation
Solve the resulting equation for the remaining variable
Substitute the value of the solved variable back into the expression from the first step to find the value of the other variable
Check the solution by substituting the values of both variables into the original equations ensuring they satisfy both equations (x=2, y=3)
Real-world applications of substitution
Identify variables in the problem and assign them to appropriate quantities (let x be the number of apples, let y be the number of oranges)
Create a of equations based on given information and relationships between variables
Ensure equations are linear with two variables (2x+3y=10, x−y=1)
Use to solve the system of equations
Follow steps outlined in the substitution method for linear systems
Interpret the solution in the context of the original problem
Ensure the solution makes sense and answers the question posed (the store sold 3 apples and 2 oranges)
Efficiency of substitution method
Often most efficient when one equation has a variable with a coefficient of 1 or -1
Allows for easy isolation of the variable, making substitution straightforward (y=2x+1)
Preferred when one equation is already solved for one of the variables
Eliminates need for the first step of the substitution process (y=3x−2)
When coefficients of variables in both equations are large or complex fractions, substitution may be easier than other methods like elimination
Avoids need to multiply equations by constants to eliminate a variable, which can lead to more complex calculations (32x+21y=5, 41x−53y=2)
Understanding Systems of Equations
An equation is a mathematical statement that two expressions are equal
A system of equations, also known as , consists of two or more equations that are considered together
The of a system is the set of all ordered pairs that satisfy all equations in the system