1. 8.1 Systems of Equations

2. A solution of a system of equations in two variables is any ordered pair that satisfies all equations in the system If in the coordinate plane, it is a point common to all graphs Linear system: system comprised entirely of linear equations Consistent system: a linear system in 2 variables with at least one solution Inconsistent system: a linear system with no solution i.e. parallel lines independent: exactly one solution intersecting lines dependent: infinitely many solutions same line

3. We can solve systems of linear equations by substitution or addition / linear combination. Ex 1) Solve by substitution 3x – 2(3x – 9) = 0 3x – 6x + 18 = 0 –3x = –18 x = 6 (6, 9)

4. Ex 2) Solve by addition 11x = –55 x = –5 (–5, 3) + 2(–5) + 3y + 1 = 0 –9 + 3y = 0 3y = 9 y = 3

5. Ex 3) Solve using substitution and sketch the graph 13 = 9(2) – y –5 = –y 5 = y (2, 5) graphing calculator y 1 = –3x 2 + 12x – 7 y 2 = 9x – 13 Find intersections  they match! 13 = 9(–1) – y 22 = –y –22 = y (–1, –22)

6. Systems are also used to model real world problems Ex 4) An animal trainer has 600 ft of fencing and wants to build an L-shaped pen with a total area of 6800 ft 2. The pen is composed of two juxtaposed rectangles of equal dimensions as shown in the diagram. Find the dimensions of the rectangles. A B y y x x Areas: xy and xy  2xy = 6800 y + x + x + (y – x)Perimeter: A + y + x + y B = 600 4y + 2x = 600 Solve 2xy = 6800 4y + 2x = 600  xy = 3400  2y + x = 300  x = 300 – 2y  (300 – 2y)y = 3400

7. Ex 4) cont… (300 – 2y)y = 3400 300y – 2y 2 = 3400 2y 2 – 300y + 3400 = 0 y 2 – 150y + 1700 = 0 Quadratic formula! y = 137.65 or 12.35 x(137.65) = 3400 x = 24.70 x(12.35) = 3400 x = 275.30 (y needs to be bigger than x) 24.70 ft × 137.65 ft

8. Homework #801 Pg 390 #1, 5, 7, 9, 11, 12, 14, 16, 18, 21, 22, 28, 34, 35, 38, 40, 42–45 HW Hint: Simple Interest Formula: I = Prt