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Published byDale Bartholomew Morrison Modified over 8 years ago

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Solving Linear Systems Substitution Method Lisa Biesinger Coronado High School Henderson,Nevada

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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.

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Example Linear System: The solution will be the values for x and y that make both equations true.

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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.

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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.

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Solving by Substitution Now we will solve for x in column 1.

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Solving by Substitution Subtract 2y from both sides.

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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.

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Solving by Substitution Always use parenthesis when substituting an expression with two terms.

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Solving the System Step 3: Simplify the equation in column 2 and solve.

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Solving by Substitution Use the distributive property and combine like terms.

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Solving by Substitution Solve for y.

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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.

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Solving by Substitution Substitute for y and solve for x. Solve for x.

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The Solution The solution to this linear system is and. The solution can also be written as an ordered pair

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Almost Finished Checking Your Solution Check your answer by substituting for x and y in both equations.

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Checking Your Answer

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Additional Examples Problem #1: Problem#2 Problem #3 Answers: #1 #2 #3

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