Solving Systems of Equations by Graphing Practice test 1 – Sept 8 LT # 1 – Sept 10

Recall: SLOPE-INTERCEPT FORM y = mx + b slope y-intercept x + 2y = 6

Convert to slope-intercept form. x + 2y = 6 2y = -x + 6 y = -1/2 x + 3

Y = -1/2 x + 3

. (1,5) y = 2x + 3 2) Obtain a second point using the slope, m. 1) Plot the point (0,3). 2) Obtain a second point using the slope, m. (for every 2 rise, 1 run) 3) Draw a line through the two points. y-intercept slope . (1,5) (0,3)  Write m as a fraction, and use rise over run, starting at the point containing the y-intercept, to plot this point. We express the slope, 2, as a fraction.

is a System of Linear Equations in two variables (x and y) The solution to the system is the ordered pair (1, 2) because it satisfies both equations.

Simultaneous Linear Equations or System of Linear Equations is a collection of linear equations with the same set of unknowns They are solved by finding values that work for both variables (x and y) at the same time (simultaneously).

Solution of a System of Equations A solution of a system of linear equations in two variables is an ordered pair (x, y) that makes BOTH equations true. A system of equations can have 0, 1, or an infinite number of solutions.

x + y = 3 y = 3x + 3 (0, 3) x + y = 1 2y = -2x + 2 (2, -1) x + y = 8 Tell whether the ordered pair is a solution of the system of equations. Justify your answer. x + y = 3 y = 3x + 3 (0, 3) x + y = 1 2y = -2x + 2 (2, -1) x + y = 8 x – 7 + y = 0 (4, 4)

Intersecting Lines 1 Solution: (3, -1)

Parallel Lines No solution: { } or Ø

Infinitely many solutions: Conciding Lines Infinitely many solutions: {(x, y)| x + y = 2} READ AS: The set of all ordered pairs (x, y) such that “x + y = 2”.

GRAPH SLOPE Y-INTERCEPT Intersecting Different Same or Different Coinciding Same Parallel

Solutions of a System of Linear Equations Consistent At least 1 solution Inconsistent No solution Dependent Infinite solutions Independent Unique/1 solution

EXISTENCE OF SOLUTION Number OF SOLUTIONS SLOPE Y-INTERCEPT Consistent Independent (One - Point of Intersection) Different Same or Different Dependent (Infinite - All points that lie on the line) Same Inconsistent No solution

Solving Systems of Linear Equations Using Graphical Method To find the solution of a system of linear equations graphically, determine the coordinates of the point of intersection of both graphs.

The Number of Solutions to a System of Two Linear Equations Existence of Solution Number of Solutions Graph Consistent and independent Exactly one ordered-pair solution Inconsistent No solution Consistent and dependent Infinitely Many Solutions

Work in Pairs Without graphing, determine the ff: a) existence of solution (consistent/inconsistent) b) number of solutions (dependent/independent) c) graph of the system (intersecting, parallel, coinciding)

2) 3x + y = 2 2x – y = 3

4) 4x + y = 2 4x + y = -3

6) 3x – 2y = 7 2x + 3y = 9

8) 3x + 2y = 4 5x + y = 2

10) 2x + 5y = 25 3x – 2y = 9

12) 3x – 4y = 25 4x – y = 16

- Review all files uploaded in Edmodo - Study Examples 1 & 2 NSM Bk2 p - Review all files uploaded in Edmodo - Study Examples 1 & 2 NSM Bk2 p. 255-256 - Review Questions # 5, 6, and 7 page 258

Online Self-Assessment http://teachers.henrico.k12.va.us/math/hcpsalgebra1/Documents/examviewweb/ev9-1.htm http://www.regentsprep.org/Regents/math/ALGEBRA/AE3/answer1.htm