3.1.2 Using Algebraic Methods to Solve Linear Systems
Key Objectives • Solve linear systems by substitution or elimination. • Classify systems with infinitely many solutions or no solution. • Write and solve linear systems. Key Terms • Substitution 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(s). • Elimination is a method used to solve systems of equations in which one variable is eliminated by adding or subtracting two equations of the system. Example 1 Solving Linear Systems by Substitution The substitution method can be used to find the exact solution of a system of equations. This method involves solving one of the equations for one of the variables and then substituting this expression into the other equation.
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