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## Solving Linear Systems

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**Solving Linear Systems**Substitution Method Lisa Biesinger Coronado High School Henderson,Nevada**Linear Systems**• A linear system consists of two or more linear equations. • The solution(s) to a linear system is the ordered pair(s) (x,y) that satisfy both equations.**Example**• Linear System: • The solution will be the values for x and y that make both equations true.**Solving the System**• Step 1: Solve one of the equations for either x or y. • For this system, the first equation is easy to solve for x because the coefficient of x is equal to 1.**Organizing Your Work**• Set up 2 columns on your paper. • Place one equation in each column. • Write the equation we are using first in column 1, and the other equation in column 2.**Now we will solve for x in column 1.**Solving by Substitution**Subtract 2y from both sides.**Solving by Substitution**Solving the System**• Step 2: Substitute your answer into the other equation in column 2. • Substituting will eliminate one of the variables in the equation.**Always use parenthesis when substituting an expression with**two terms. Solving by Substitution**Solving the System**• Step 3: Simplify the equation in column 2 and solve.**Use the distributive property and combine like terms.**Solving by Substitution**Solve for y.**Solving by Substitution**Solving the System**• Step 4: Substitute your answer in column 2 into the equation in column 1 to find the value of the other variable.**Substitute for y and solve for x. Solve for x.**Solving by Substitution**The Solution**• The solution to this linear system is and . • The solution can also be written as an ordered pair**Almost FinishedChecking Your Solution**• Check your answer by substituting for x and y in both equations.**** Checking Your Answer**Problem #1:**Problem#2 Problem #3 Answers: #1 #2 #3 Additional Examples