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

2a)Graph the following system of linear inequalities: − 12x + 4y > − 12 y ≤ − 2x 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

a)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 True * Shade region that contains the point (0, 0). Need to shade appropriate region.

2b)Determine if (2, − 1) is a solution to the system of inequalities. − 12x + 4y > − 12 y ≤ − 2x 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

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

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

5.Choose 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.

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

There are 18 coins in all. 7.A collection of dimes and quarters is worth $2.85. 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) = − d + 25q = q = 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 How many of each type of coin are there?