Stand Quietly Lesson 5 1Solving Systems of Equations

Stand Quietly

Lesson 5. 1_Solving Systems of Equations By Graphing Students will be able to find the solution(s) of a system of linear equations by graphing

Warm-Up #12 (3/7/2017) 4

Homework (3/7/2017) Worksheet: Solving Systems of Equations by Graphing pg 1 and 2 (ALL)

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4 A solution to a system of equations is an ordered pair that satisfy all the equations in the system. 4 A system of linear equations can have: • 1. Exactly one solution • 2. No solutions • 3. Infinitely many solutions 6

Inconsistent Dependent One solution No solution Lines intersect Lines are parallel Infinite number of solutions Consistent Coincide-Same line 7

There are 3 ways to solve systems of linear equations: 41. By graphing 42. By substitution 43. By elimination 8

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4 Solving Systems by Graphing: 4 When solving a system by graphing: 1. Change the equations into y = mx + b so you can see the slope (m) and the y-intercept (b) 2. Graph both equations 3. Find the intersection point (break-even point) and that will determine the solution or solutions to the system of equations. 10

4 Determine Without Graphing: 4 Once the equations are in slope-intercept form, compare the slopes and intercepts. 4 One solution – the lines will have different slopes. 4 No solution – the lines will have the same slope, but different intercepts. 4 Infinitely many solutions – the lines will have the same slope and the same intercept. 11

Determine Without Graphing: 4 Given the following lines, determine what type of solution exists, without graphing. 4 Equation 1: 3 x = 6 y + 5 4 Equation 2: y = (1/2)x – 3 4 Writing each in slope-intercept form (solve for y) 4 Equation 1: y = (1/2)x – 5/6 4 Equation 2: y = (1/2)x – 3 4 Since the lines have the same slope but different yintercepts, there is no solution to the system of equations. The lines are parallel. 12

2 x – y = 2 x + y = -2 2 x – y = 2 -y = -2 x + 2 y = 2 x – 2 x + y = -2 y = -x - 2 Different slope, different intercept! 13

3 x + 2 y = 3 3 x + 2 y = -4 3 x + 2 y = 3 2 y = -3 x + 3 y = -3/2 x + 3/2 3 x + 2 y = -4 2 y = -3 x -4 y = -3/2 x - 2 Same slope, different intercept!! 14

x – y = -3 2 x – 2 y = -6 x – y = -3 -y = -x – 3 y = x + 3 2 x – 2 y = -6 -2 y = -2 x – 6 y = x + 3 Same slope, same intercept! Same equation!!