University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
Views:

31

Pages:

1
Author:

gildnar99xu

Mini-Lecture 4.1 Solving Systems of Linear Equations by Graphing Learning Objectives: 1. Determine if an ordered pair is a solution of a system of equations in two variables. 2. Solve a system of linear equations by graphing. 3. Without graphing, determine the number of solutions of a system. Examples: 1. Determine whether the ordered pair is a solution of the system of linear equations. ⎧ x + y = −9 ⎩x − y = 1 b) ( −5, −3) ⎨ ⎧4 x = 4 − y ⎩ 2 x = −12 − 4 y d) ( −3,1) ⎨ a) ( −4, −5 ) ⎨ c) ( 2, −4 ) ⎨ ⎧ 2 x + y = −7 ⎩3 x + 2 y = − 9 ⎧3 x = 10 − y ⎩4 x = 15 − 3 y 2. Solve each system of linear equations by graphing. Note: All systems have a solution. ⎧ 4 x + y = −4 a) ⎨ ⎩5 x + 2 y = − 2 c) ⎧x = 6 ⎪ ⎨1 ⎪⎩ 6 x − y = 1 ⎧3 x + 2 y = 22 b) ⎨ ⎩ 2 x + 4 y = 28 d) ⎧2 x + 5 y = 32 ⎨ ⎩3 y = 20 − 2 x 3. Without graphing, determine the number of solutions of a system. Note: the systems have no solution or an infinite number of solutions. a) ⎧4 x − 16 y = 12 ⎪ ⎨ 1 3 ⎪⎩ y = 4 x − 4 ⎧− x = y b) ⎨ ⎩x = 6 − y Teaching Notes: • • • • Many students need to be reminded to use graph paper and be very neat with their graphing skills. Remind students to substitute their solution into the original equations to check their results. Many students get confused between consistent and inconsistent systems and its meaning for the solution. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) yes; 1b) no; 1c) yes; 1d) no; 2a) – 2d) see mini-lecture graphing answers; 3a) infinite; 3b) no solution