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Published bySade Sarff Modified about 1 year ago

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EXAMPLE 1 Use the substitution method Solve the system using the substitution method. 2x + 5y = –5 x + 3y = 3 Equation 1 Equation 2 SOLUTION STEP 1 Solve Equation 2 for x. x = –3y + 3 Revised Equation 2

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EXAMPLE 1 Use the substitution method STEP 2 Substitute the expression for x into Equation 1 and solve for y. 2x +5y = –5 2(–3y + 3) + 5y = –5 y = 11 Write Equation 1. Substitute –3y + 3 for x. Solve for y. STEP 3 Substitute the value of y into revised Equation 2 and solve for x. x = –3y + 3 x = –3(11) + 3 x = –30 Write revised Equation 2. Substitute 11 for y. Simplify.

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EXAMPLE 1 Use the substitution method CHECK Check the solution by substituting into the original equations. 2(–30) + 5(11) –5 = ? Substitute for x and y. = ? –30 + 3(11) 3 Solution checks. 3 = 3 –5 = –5 The solution is (– 30, 11). ANSWER

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EXAMPLE 2 Use the elimination method Solve the system using the elimination method. 3x – 7y = 10 6x – 8y = 8 Equation 1 Equation 2 SOLUTION Multiply Equation 1 by – 2 so that the coefficients of x differ only in sign. STEP 1 3x – 7y = 10 6x – 8y = 8 –6x + 14y = 220 6x – 8y = 8

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EXAMPLE 2 Use the elimination method STEP 2 Add the revised equations and solve for y. 6y = –12 y = –2 STEP 3 Substitute the value of y into one of the original equations. Solve for x. 3x – 7y = 10 3x – 7(–2) = 10 3x + 14 = 10 x =x = 4 3 – Solve for x. Simplify. Substitute –2 for y. Write Equation 1.

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EXAMPLE 2 Use the elimination method The solution is (, –2 ) 4 3 – ANSWER CHECK You can check the solution algebraically using the method shown in Example 1. You can also use a graphing calculator to check the solution.

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1.4x + 3y = –2 x + 5y = –9 Solve the system using the substitution or the elimination method. GUIDED PRACTICE for Examples 1 and 2 The solution is (1,–2). ANSWER 2. 3x + 3y = –15 5x – 9y = 3 The solution is (, –2) 3 – ANSWER

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Solve the system using the substitution or the elimination method. GUIDED PRACTICE for Examples 1 and x – 6y = 9 –4x + 7y = –16 The solution is (11, 4) ANSWER

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