Solving Linear Systems by Substitution - Flagler County Schools

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138 Algebra 1 Notetaking Guide • Chapter 7 Example 2 The <strong>Substitution</strong> Method Solve the linear system. 2x 5y 13 Equation 1 x 3y 1 Equation 2 Solution 1. Solve for x in Equation 2 because it is easy to isolate x. x 3y 1 Revised Equation 2 2. Substitute 3y 1 for x in Equation 1 and solve for y. 2x 5y 13 Write Equation 1. 2( 3y 1 ) 5y 13 Substitute for x. 6y 2 5y 13 Distribute. 11y 2 13 Simplify. 11y 11 Add 2 to each side. y 1 Solve for y. 3. To find the value of x, substitute 1 for y in the revised Equation 2 and solve for x. x 3y 1 Write revised Equation 2. x 3(1) 1 Substitute for y. x 4 Simplify. 4. Check that ( 4 , 1 ) is a solution <strong>by</strong> substituting 4 for x and 1 for y in each of the original equations. Equation 1 Equation 2 2x 5y 13 x 3y 1 2( 4 ) 5( 1 ) 13 4 3( 1 ) 1 8 5 13 4 3 1 13 13 1 1 Answer The solution is ( 4 , 1 ).
Checkpoint Tell which equation you would use to isolate a variable. Explain your reasoning. 1. x 2y 0 2. 4x 2y 10 x 8y 5 7xy12 I would isolate x in the I would isolate y in the first equation because it second equation because is easy to do so and the it is easier to do so than value is easy to substitute to isolate y in the first in the other equation. equation or x in either equation. Use the substitution method to solve the linear system. 3. y x 1 4. y 5x 3 x 5y 15 3x 2y 8 (5, 4) (2, 7) Lesson 7.2 • Algebra 1 Notetaking Guide 139
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Solving Linear Systems by Substitution - Flagler County Schools

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