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Lesson Menu Five-Minute Check (over Lesson 9–6) Main Idea and Vocabulary Example 1:One Solution Example 2:No Solution Example 3:Infinitely Many Solutions Example 4:Writing and Solving Systems of Equations

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Main Idea/Vocabulary Solve systems of equations by graphing. system of equations

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Example 1 One Solution Solve the systems y = 3x – 2 and y = x + 1 by graphing. Graph each equation on the same coordinate plane. The graphs appear to intersect at (1.5, 2.5). Check in both equations by replacing x with 1 and y with 1.

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Example 1 One Solution Check y= 3x – 2 y = x + 1 2.5 = 3(1.5) – 22.5 = 1.5 + 1 ?? 2.5= 4.5 – 22.5 = 2.5 ? 2.5= 2.5 Answer: The solution of the system is (1.5, 2.5).

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1.A 2.B 3.C 4.D Example 1 Solve the systems y = x – 4 and y = 2x – 6 by graphing. A.B. C.D.

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Example 2 No Solution Solve the systems y = 2x – 1 and y = 2x by graphing. The graphs appear to be parallel lines. Answer: Since there is no coordinate point that is a solution of both questions, there is no solution for the system of equations.

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1.A 2.B 3.C 4.D Example 2 Solve the systems y = –3x – 2 and y = –3x + 4 by graphing. A.B. C.D.

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Example 3 Infinitely Many Solutions Solve the systems y = 3x – 2 and y – 2x = x – 2 by graphing. Write y – 2x= x – 2 in slope-intercept form. y – 2x= x – 2Write the equation. y – 2x + 2x= x – 2 + 2x Add 2x to both sides. y= 3x – 2Simplify. Both equations are the same. Graph the equation.

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Example 3 Infinitely Many Solutions Answer: The solution of the system is all ordered pairs of the points on the line y = 3x – 2.

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1.A 2.B 3.C 4.D Example 3 Solve the systems y = 2x – 5 and y + 2 = 2x – 3 by graphing. A.B. C.D.

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Example 4 Writing and Solving Systems of Equations Fourteen boys and girls are on a soccer team. The number of girls is two more than the number of boys. Write a system of equations that represents the number of boys and girls. Solve the system of equations by graphing. Let x = the number of boys and y = the number of girls. number of boys plus number of girls equals fourteen xy14+= number of girls istwo more than number of boys y2x=+

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Example 4 Writing and Solving Systems of Equations So, the system of equations is x + y = 14 and y = x + 2. Write x + y = 14 in slope-intercept form. x + y= 14Write the equation. x + y – x= 14 – x Subtract x from both sides. y= 14 – x Simplify. Graph each equation on the same coordinate plane.

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Example 4 Writing and Solving Systems of Equations The lines appear to intersect at (6, 8). y= 14 – xy = x + 2 14 = 148 = 8 8= 14 – 68 = 6 + 2 ?? Answer: The solution of the system is (6, 8). So, there are 6 boys and 8 girls on the team. Check Check in both equations by replacing x with 6 and y with 8.

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1.A 2.B 3.C 4.D Example 4 A.c + d = 6 d = c + 2 B.c + d = 6 d = c – 2 C.d + c = 8 6 – d = c D.d + c = 8 d – 4 = c PETS Faith has six pets, all of which are cats and dogs. The number of dogs d is two less than the number of cats c. Which system of equations represents the number of cats and dogs Faith has?

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End of the Lesson

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Resources Five-Minute Check (over Lesson 9–6) Image Bank Math Tools Slope and Intercept

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1.A 2.B 3.C 4.D Five Minute Check 1 State the slope and the y-intercept for the graph of the equation y = 2x + 1. (over Lesson 9-6) A. B. C. D.

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1.A 2.B 3.C 4.D Five Minute Check 2 (over Lesson 9-6) State the slope and the y-intercept for the graph of the equation y = 3x + 2. A. B. C. D.

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1.A 2.B 3.C 4.D Five Minute Check 3 (over Lesson 9-6) A.m = –2; b = 4.5 B.m = –2; b = –4.5 C.m = 4.5; b = 2 D.m = 4.5; b = –2 State the slope and the y-intercept for the graph of the equation y = –2x + 4.5.

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1.A 2.B 3.C 4.D Five Minute Check 4 (over Lesson 9-6) A.m = –4; b = 3 B.m = –3; b = 4 C.m = 3; b = –4 D.m = 4; b = –3 State the slope and the y-intercept for the graph of the equation 3x – y = 4.

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1.A 2.B 3.C 4.D Five Minute Check 5 (over Lesson 9-6) A.the price of apples per pound B.the total price of apples C.total number of apples D.the total weight of the apples picked The total price of apples (y) at an orchard can be calculated with the equation 1.12x + 5 = y, where x is the number of pounds of apples picked. What does the slope represent?

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1.A 2.B 3.C 4.D Five Minute Check 6 (over Lesson 9-6) What is the equation of the graph shown? A. B. C. D.

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