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**Use addition to eliminate a variable**

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

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**Use addition to eliminate a variable**

EXAMPLE 1 Use addition to eliminate a variable STEP 3 Substitute 3 for y in either equation and solve for x. 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).

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**Use addition to eliminate a variable**

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

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**Use subtraction to eliminate a variable**

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

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**Use subtraction to eliminate a variable**

EXAMPLE 2 Use subtraction to eliminate a variable STEP 3 Substitute 4 for x in either equation and solve for y. 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).

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**Solve the linear system: 8x – 4y = –4 4y = 3x + 14**

EXAMPLE 3 Arrange like terms 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 8x – 4y = –4 4y = 3x + 14 3x + 4y = 14 STEP 2 Add the equations. 5x = 10 STEP 3 Solve for x. x = 2

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**Substitute 2 for x in either equation and solve for y.**

EXAMPLE 3 Arrange like terms STEP 4 Substitute 2 for x in either equation and solve for y. 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).

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

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

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

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

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

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

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EXAMPLE 1 Solve a quadratic equation having two solutions Solve x 2 – 2x = 3 by graphing. STEP 1 Write the equation in standard form. Write original equation.

EXAMPLE 1 Solve a quadratic equation having two solutions Solve x 2 – 2x = 3 by graphing. STEP 1 Write the equation in standard form. Write original equation.

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