2. 3456-4-3-271-7-6-52 1 2 3 4 5 6 7 -2 -3 -4 -5 -6 -7 1.Solve the system of equations using the graphing method. y = x – 5 x + 2y = − 4 Find the x and y intercepts. y – int.: (0, − 2) x – int.: (− 4, 0) Notice, the y-int. is (0, − 5) and the slope = 1 y = x – 5 Find the y intercept and slope. Answer: (2, − 3) x + 2y = − 4 © 2007-09 by S-Squared, Inc. All Rights Reserved.

3. 2a)Graph the following system of linear inequalities. − 12x + 4y > − 12 y ≤ − 2x + 3 3456-4-3-271-7-6-52 1 2 3 4 5 6 7 -2 -3 -4 -5 -6 -7 Find the x and y intercepts. y – int.: (0, − 3) x – int.: ( 1, 0) Notice, the y-int. is (0, 3) and the slope = − 2 y = − 2x + 3 Find the y intercept and slope. − 12x + 4y > − 12

4. 3456-4-3-271-7-6-52 1 2 3 4 5 6 7 -2 -3 -4 -5 -6 -7 2a)Graph the following system of linear inequalities. − 12x + 4y > − 12 y ≤ − 2x + 3 Use (0, 0) as a test point. y ≤ − 2x + 3 − 12x + 4y > − 12 − 12(0) + 4(0) > − 12 0 > − 12 True (0) ≤ − 2(0) + 3 0 ≤ 3 True * Shade region that contains the point (0, 0). Need to shade appropriate region.

5. 2b)Determine if (2, − 1) is a solution to the inequality. − 12x + 4y > − 12 y ≤ − 2x + 3 3456-4-3-271-7-6-52 1 2 3 4 5 6 7 -2 -3 -4 -5 -6 -7 Substitute (2, − 1) into inequalities. y ≤ − 2x + 3 − 12x + 4y > − 12 − 12(2) + 4(− 1) > − 12 False (− 1) ≤ − 2(2) + 3 − 1 ≤ − 1 True * Since the point does not work for both inequalities, it is not a solution. − 28 > − 12 Not a solution

6. 3.Solve the system of equations using the substitution method. 2x + y = − 5 x + 4y = 1 y = − 2x – 5 Substitute x + 4(− 2x – 5) = 1 x – 8x – 20 = 1 − 7x – 20 = 1 − 7x = 21 x = − 3 Find y 2x + y = − 5 Solve for y Distribute Combine Substitute 2(− 3) + y = − 5 Multiply − 6 + y = − 5 y = 1 Final Answer: (− 3, 1) Solve

7. 4.Solve the following system of equations using the linear combination method. 3x – 2y = 5 x + 4y = − 3 2(3x – 2y = 5) 6x – 4y = 10 x + 4y = − 3 7x = 7 x = 1 Multiply Other Equation Add Equations Find y x + 4y = − 3 Substitute 1 + 4y = − 3 4y = − 4 y = − 1 Final Answer: (1, − 1) Solve

8. 5.Choose the any method to solve the system of linear equations. 5x + y = − 8 15x + 3y = − 24 y = − 5x – 8 Substitute 15x + 3(− 5x – 8) = − 24 15x – 15x – 24 = − 24 0x – 24 = − 24 − 24 = − 24 Solve for y Distribute Combine Final Answer: Infinite points of intersection Substitution Method Since what is left is a true statement, we know the lines are the same.

9. Write two Equations: 7x = y + 5 Subtract y: 6.The sum of two numbers is 19. Seven times the first number is five more than the second. What are the two numbers? x + y = 19 Assign Variables: Let, x = the first # y = the second # 7x – y = 5 x + y = 19 8x = 24 x = 3 x + y = 19 3 + y = 19 y = 16 Substitute to find y: The first number is 3 The second number is 16 – y The sum of two numbers is 19. Seven times the first number is five more than the second. Combination Method

10. 7.A collection of dimes and quarters is worth $2.85. There are 18 coins in all. How many of each type of coin are there? A collection of dimes and quarters is worth $2.85. There are 18 coins in all. ( )100 Write two Equations:.10d +.25q = 2.85 Multiply by 100: d + q = 18 Assign Variables: Let, d = the # of dimes q = the # of quarters 10d + 25q = 285 d + q = 18 Multiply by − 10: − 10d + (− 10q) = − 180 10d + 25q = 285 15q = 105 q = 7 d + q = 18 d + 7 = 18 d = 11 Substitute to find d: There are 7 quarters and 11 dimes. Work hard for you Combination Method