Table of Contents Topic Page # A Absolute Value Less ThAND B Absolute Value GreatOR Than Two Variable Inequalities Solve Systems By Graphing 76

A system of linear equations, consists of two or more linear equations in the same variables. You can solve a system of linear equations by graphing them in the same coordinate plane. The solution of the system is the point where the two graphs intersect. The solution found using graphical methods should be checked algebraically.

Example 1: Solve by graphing y = x – 2 bmbm (0, -2) 1111 y = -¼x – 2 bmbm (0, -2) 4 (0, -2)

(0, –2) Solution to the system Plug in x and y in both equations

= -2 (0, –2) -2 = (-2) = = -8 solution

STEPS for solving linear systems by graphing 1. Solve for y = mx + b 2. Graph both lines with b/m chart 3. Where lines cross is solution 4. Check your solution in both equations

Example 2: Solve the system by graphing and check your solution. y = 1/3x – 2 bmbm (0, -2) 1313 y = 2/3x – 1 bmbm (0, -1) 2323 (-3, -3)

-3 – 3(-3) = 6 6 = 6 2(-3) – 3(-3) = 3 3 = 3 solution = = 3

SKIP

y = -x + 6 bmbm (0, 6) 1 y = x – 2 bmbm (0, -2) 1111 (4, 2)

2 = = 2 2 = 4 – 2 2 = 2 solution

y = x bmbm (0, 0) 1111 y = 3x – 2 bmbm (0, -2) 3131 (1, 1)

1 = 1 -3(1) + 1 = = -2 solution = -2

Example 3: Tell whether the ordered pair is a solution of the linear system.

-(-8) + 4(4) = = -8 Not a solution = -8

3(7) + 2(-6) = 9 9 = 9 -4(7) - 3(-6) = = -10 solution 21 – 12 = = -10

3(4) + (-6) = -6 6 = -6 Not a solution 12 – 6 = -6

½(4) – ¾(-2) = 7/2 7/2 = 7/2 4(4) + 3/8(-2) = 61/4 61/4 = 61/4 solution 2 + 3/2 = 7/2 16 – ¾ = 61/4

Example 4: Rental business: A business rents in-line skates and bicycles. During one day, the business has a total of 25 rentals and collects $450 for the rentals. Find the number of pairs of skates rented and the number of bicycles rented. a) Solution: Step 1: Write a linear system. Let x be the number of pairs of skates rented and let y be the number of bicycles rented. x + y = 25 15x + 30y = 450

Step 2: Graph both equations (hint: count by 5) (graph by using x and y intercepts) x + y = 25 15x + 30y = 450

Step 3: Estimate the point of intersection (20,5)

Step 4: Check whether the point is a solution = 25 15(20) + 30(5) = = 450 solution 25 = = 450 (20, 5) x + y = 25 15x + 30y = 450

b) Suppose the business has a total of 20 rentals and collects $420. Find the number of bicycles rented. SKIP