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Published byWinfred McDowell Modified over 7 years ago

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7 = 7 SOLUTION EXAMPLE 1 Check the intersection point Use the graph to solve the system. Then check your solution algebraically. x + 2y = 7 Equation 1 3x – 2y = 5 Equation 2 The lines appear to intersect at the point (3, 2). CHECK Substitute 3 for x and 2 for y in each equation. x + 2y = 7 3 + 2(2) = ? 7

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ANSWER Because the ordered pair (3, 2) is a solution of each equation, it is a solution of the system. EXAMPLE 1 Check the intersection point 3x – 2y = 5 5 = 5 3(3) – 2(2 ) 5 = ?

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EXAMPLE 2 Use the graph-and-check method Solve the linear system : –x + y = –7 Equation 1 x + 4y = –8 Equation 2 SOLUTION STEP 1 Graph both equations.

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EXAMPLE 2 STEP 2 Use the graph-and-check method Estimate the point of intersection. The two lines appear to intersect at (4, – 3). STEP 3 Check whether (4, –3) is a solution by substituting 4 for x and –3 for y in each of the original equations. Equation 1 –x + y = –7–x + y = –7 –7 = –7 –(4) + (–3) –7 = ? Equation 2 x + 4y = –8x + 4y = –8 –8 = –8 4 + 4(–3) –8 = ?

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ANSWER Because (4, –3) is a solution of each equation, it is a solution of the linear system. EXAMPLE 2 Use the graph-and-check method

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EXAMPLE 2 Use the graph-and-check method Solve the linear system by graphing. Check your solution. GUIDED PRACTICE for Examples 1 and 2 –5x + y = 0 1. 5x + y = 10 ANSWER (1, 5)

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EXAMPLE 2 Use the graph-and-check method Solve the linear system by graphing. Check your solution. GUIDED PRACTICE for Examples 1 and 2 2x + y = 4 –x + 2y = 3 2. ANSWER (1, 2)

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EXAMPLE 2 Use the graph-and-check method Solve the linear system by graphing. Check your solution. GUIDED PRACTICE for Examples 1 and 2 3x + y = 3 x – y = 5 3. ANSWER (2, 3)

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