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EXAMPLE 1

Begin by graphing both equations, as shown at the right. From the graph, the lines appear to intersect at ( 3, –4 ). You can check this algebraically as follows. EXAMPLE 1. Solve a system graphically. Graph the linear system and estimate the solution. Then check the solution algebraically.

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EXAMPLE 1

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  1. Begin by graphing both equations, as shown at the right. From the graph, the lines appear to intersect at (3, –4). You can check this algebraically as follows. EXAMPLE 1 Solve a system graphically Graph the linear system and estimate the solution. Then check the solution algebraically. 4x + y = 8 Equation 1 2x – 3y = 18 Equation 2 SOLUTION

  2. 4(3) +(–4) 8 8 = 8 2(3) – 3(– 4) 18 6 + 12 18 12 –4 8 18 = 18 ? ? ? ? = = = = EXAMPLE 1 Solve a system graphically Equation 2 Equation 1 4x+ y= 8 2x– 3y= 18 The solution is (3, –4).

  3. 1. 3x + 2y = –4 for Example 1 GUIDED PRACTICE Graph the linear system and estimate the solution. Then check the solution algebraically. ANSWER The solution is (–2, 1).

  4. 2. 4x – 5y = –10 for Example 1 GUIDED PRACTICE Graph the linear system and estimate the solution. Then check the solution algebraically. ANSWER The solution is (–5, –2).

  5. 3. 8x – y = 8 for Example 1 GUIDED PRACTICE Graph the linear system and estimate the solution. Then check the solution algebraically. ANSWER The solution is (0, –8).

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