University:
Missouri State University
Course:
MTH 103 | Intermediate Algebra
Academic year:

2020
Views:

317

Pages:

2
Author:

staipsedilsi90

ALGEBRA 2 Name: KEY Date: 3.1 Solving Linear Systems by Graphing Vocabulary: A linear system consists of two equations with two variables in each, x and y. A Solution of a system is an ordered pair(xy) that satisfies BOTH equations. When solving systems by graphing, the solution is the intersection point Finding Solutions of Linear Systems: 1. Show that (2, 3) is a solution of: 3x - y =3( x + 2y =8| 3(2)-3-322+2(3)-8 2+6=8 8-8 6-3-3 3-3 XY 2. Is (0, 8) a solution to the following system? y = - 3/2 * x + 80 y = - 5x + 3(2) 8 = - 3/2 * (0) + 8 8=0+8 8-8 828--5(0)+3 8=0+3 8=3 NO Solving Linear Systems by Graphing: Solve the following linear systems by graphing. 3. 3x - y = 3 x + 2y =8( 4. y = - x + 3 y = x + 7(2) 3x - y = 3 - y = - 3x + 3 sqrt = 3x - 3 (2,3) (-2,5) x + 2y = 8 2y = - x + 8 y = - 1/2 * x + 4 5. x - 3y = 1 - x + y = - (2) x - 3y = 1 - 3y = - x + 1 y = 1/3 * x - 1/3 - x + y = - 1 y = x - 1 (1,0) Systerns with Infinitely Many or No Solutions: 7. 2x - y =1(0 - 4x + 2y = - 2 2x - y = 1 y = - 2x + 1 y = 2k - 1 - 4x + 2y = - 2 2y - 4x - 2 = 2x - 1 Same line Infinitely Many Solutions! 6. - x + 4y = 2 aligned 2x - 3y =b( aligned - x + 4y = 2 4y = x + 2 y = 1/4 * x + 1/2 (6,2) 2x - 3y = 6 - 3y = - 2x + 6 y = 2/3 * x - 2 8. y = - 1/2 * x + 2 x + 2y =-6| x + 2y = - 6 2y = - x - 6 Y = - 1/2 * x - 3 Parallel Lines Same slopes/different Y-intercepts No Solution! Summary of Solutions to Linear Systems: Exactly One Infinitely Many No Solutions * different slopes * lines intersect at only 1 point * same slopes and y-intercepts * lines are identical parallel lines same slopes different y-intercepts *Most popular! Practice from the Textbook: Matching Graphs Match the linear system with its graph. Tell how many solutions the system has. 2x - y = 5 B - 4x + 2y = - 10 A. - x + 5y = 80 2x - 10y = 6(2) B. 4x - 7y = 270 C - 6r - 9y = - 21(2) C 23.) 2x - y = 5 - y = - 2x + 5 y = 2x - 5 ② - 4x + 2y = - 10 2y = 4x - 10 y = 2x - 5 Same line Infinitely Many Solutions B 24) - x + 5y = 8 5y = x + 8 y = 1/5 * x + 8/5 2x - 10y = 6 - 10y = - 2x + 6 y = 1/5 * x - 3/5 *Same slopes/different y-int A 25) 4x - 7y = 27 - 7y = - 4x + 27 Y = 4/7 * x - 27/7 b = 3 6/7 ② - 6x - 9y = - 21 - 9y = 6x - 21 y = - 2/3 * x + 7/3 b = 2 1/3 #different slopes one solution C