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3.1 WARM-UP Graph each of the following problems 1. 4. 2. 5. 6. 3.

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**Solve Linear Systems by Graphing**

3.1 Solve Linear Systems by Graphing A system of linear equations is 2 or more equations that intersect at the same point or have the same solution. You can find the solution to a system of equations in several ways. The one you are going to learn today is to find a solution by graphing. The solution is the ordered pair where the 2 lines intersect. In order to solve a system, you need to graph both equations on the same coordinate plane and then state the ordered pair where the lines intersect.

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**Consistent – a system that has at least one solution**

Classifying Systems Consistent – a system that has at least one solution Inconsistent – a system that has no solutions Independent – a system that has exactly one solution Dependent – a system that has infinitely many solutions Lines intersect at one point: consistent and independent Lines coincide; consistent and dependent Lines are parallel; inconsistent

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**GUIDED PRACTICE Graph each system and then estimate the solution.**

4x – 5y = -10 2x – 7y = 4 3x + 2y = -4 x + 3y = 1 4x – 5y = -10 2x – 7y = 4 3x + 2y = -4 x + 3y = 1 -5y = -4x -10 -7y = -2x + 4 3y = -x + 1 2y = -3x - 4 From the graph, the lines appear to intersect at (–2, 1). From the graph, the lines appear to intersect at (–5, –2). Consistent & Independent Consistent & Independent

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**GUIDED PRACTICE 8x – y = 8 3x + 2y = -16 8x – y = 8 3x + 2y = -16**

From the graph, the lines appear to intersect at (0, –8). Consistent & Independent

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**the system has no solution**

Solve the system. Then classify the system as consistent and independent,consistent and dependent, or inconsistent. 2x + y = 4 4x – 3y = 8 8x – 6y = 16 2x + y = 1 2x + y = 4 2x + y = 1 4x – 3y = 8 8x – 6y = 16 y = -2x + 1 y = -2x + 4 – 3y = -4x + 8 – 6y = -8x + 16 (the lines have the same slope) (the equations are exactly the same) the system has no solution inconsistent. consistent and dependent. The system has infinite solutions

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**Consistent and independent**

Solve the system. Then classify the system as consistent and independent, consistent and dependent, or inconsistent. 2x + 5y = 6 4x + 10y = 12 2x + 5y = 6 4x + 10y = 12 A. Same equation Infinite solutions Consistent and independent 10y = -4x + 12 5y = -2x + 6 3x – 2y = 10 3x – 2y = 2 B. 3x – 2y = 10 3x – 2y = 2 Same slope // lines no solution inconsistent 2y = – 3x + 10 2y = – 3x + 2 (–1, 3) consistent independent C. – 2x + y = 5 y = – x + 2 – 2x + y = 5 y = – x + 2 y = 2x + 5

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**HOMEWORK 3.1 P.156 #3-10 and board work C. – 2x + y = 5 y = – x + 2**

(–1, 3) consistent independent C. – 2x + y = 5 y = – x + 2 – 2x + y = 5 y = – x + 2 y = 2x + 5 Is (-1,3) the correct solution? – 2x + y = 5 y = – x + 2 3 = – (-1) + 2 – 2(-1) + (3)= 5 3 = 1 + 2 ☺ 2 + 3 = 5 ☺ HOMEWORK 3.1 P.156 #3-10 and board work

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(3, 3) No solution (-1, 1) Infinite solutions

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**Consistent, independent 14.**

Solve each system of equations by graphing. Indicate whether the system is Consistent- Independent, Consistent-Dependent, or Inconsistent (-1, 3) Consistent, independent 5. no solution inconsistent, 6. 5. 6. 8. y = 3x - 2 Infinite solutions Consistent, dependent 7. (1, 2) Consistent, independent 8. 7. 9. y = x + 6 y = x + 5 No solutions Inconsistent 10. y= -x + 6 y = -x + 6 Infinite solutions Consistent, dependent 10. 9. 11. y = ½ x (2, 1) Consistent, independent 12. y = 1/2x + 4 Consistent, dependent Infinite solutions 12. 11. 13. y = -2x + 4 y = x - 2 (2, 0) Consistent, independent 14. y = -x + 2 y = -x + 6 No solutions inconsistent 14. 13. 15. y = -3x + 2 Consistent, dependent Infinite solutions 16. y = -2x + 4 y = 6x - 4 (1, 1) Consistent, independent 16. 15.

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