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Do Now Pass out calculators. Solve the following system by graphing: Graph paper is in the back. 5x + 2y = 9 x + y = -3 Solve the following system by using substitution: 11x – 7y = - 14 x – 2y = -4

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Objective: To solve systems of equations using elimination (adding or subtracting).

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Use addition to eliminate a variable EXAMPLE 1 Solve the linear system: 2x + 3y = 11 –2x + 5y = 13 Equation 1 Equation 2 SOLUTION Add the equations to eliminate one variable. 2x + 3y = 11 –2x + 5y = 13 Solve for y. 8y = 24 y = 3 STEP 1 STEP 2

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Use addition to eliminate a variable EXAMPLE 1 2x + 3y = 11 Write Equation 1 2x + 3(3) = 11 Substitute 3 for y. x = 1 Solve for x. ANSWER The solution is (1, 3). Substitute 3 for y in either equation and solve for x. STEP 3

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Use addition to eliminate a variable EXAMPLE 1 2x + 3y = 11 11 = 11 Substitute 1 for x and 3 for y in each of the original equations. CHECK 2(1) + 3(3) = 11 ? 2x + 5y = 13 13 = 13 2(1) + 5(3) = 13 ?

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Use subtraction to eliminate a variable EXAMPLE 2 Solve the linear system: 4x + 3y = 2 Equation 1 5x + 3y = –2 Equation 2 SOLUTION Subtract the equations to eliminate one variable. 4x + 3y = 2 5x + 3y = –2 Solve for x. – x = 4 STEP 1 STEP 2 x = 4

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Use subtraction to eliminate a variable EXAMPLE 2 4x + 3y = 2 Write Equation 1. 4(–4) + 3y = 2 Substitute –4 for x. y = 6 Solve for y. ANSWER The solution is (–4, 6). Substitute 4 for x in either equation and solve for y. STEP 3

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Arrange like terms EXAMPLE 3 Solve the linear system: 8x – 4y = –4 Equation 1 4y = 3x + 14 Equation 2 SOLUTION STEP 1 Rewrite Equation 2 so that the like terms are arranged in columns. 8x – 4y = –4 4y = 3x + 14 8x – 4y = –4 3x + 4y = 14 STEP 2 Add the equations. 5x = 10 STEP 3 Solve for x. x = 2

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Arrange like terms EXAMPLE 3 4y = 3x + 14 Write Equation 2. 4y = 3(2) + 14 Substitute 2 for x. y = 5 Solve for y. ANSWER The solution is (2, 5). STEP 4 Substitute 2 for x in either equation and solve for y.

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GUIDED PRACTICE for Example 1,2 and 3 Solve the linear system: 4x – 3y = 5 –2x + 3y = –7 ` 1. ANSWER (–1, –3)

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GUIDED PRACTICE for Example 1,2 and 3 Solve the linear system: 5x + 2y = 4 5x – 6y = 8– 2. ANSWER (2, –3)

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GUIDED PRACTICE for Example 1,2 and 3 Solve the linear system: 6x – 4y = 14 3x + 4y = 1 – 3. ANSWER (5, 4)

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GUIDED PRACTICE for Example 1,2 and 3 Solve the linear system: 7x – 2y = 5 7x – 3y = 4 4. ANSWER (1, 1)

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GUIDED PRACTICE for Example 1,2 and 3 Solve the linear system: 3x + 4y = –6 5. = 3x + 6 2y2y ANSWER (–2, 0)

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GUIDED PRACTICE for Example 1,2 and 3 Solve the linear system: 2x + 5y = 12 6. = 4x + 6 5y5y ANSWER (1, 2)

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