Mini-Lecture 4.2: Solving Systems of Linear Equations by Substitution | Montgomery College - Edubirdie

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

2023
Views:

373

Pages:

1
Author:

Alma Hester

Mini-Lecture 4.2 Solving Systems of Linear Equations by Substitution Learning Objectives: 1. Use the substitution method to solve a system of linear equations. Examples: 1. Solve each system of equations by the substitution method. Note: the following systems have one equation already solved for one variable. a) ⎧x + y = 9 ⎨ ⎩ y = 2x b) ⎧x = y − 2 ⎨ ⎩x + y = 6 Solve each system of equations by the substitution method. ⎧x + 6 y = 2 c) ⎨ ⎩4 x + 5 y = −11 d) ⎧x − 3y = 3 ⎨ ⎩ −5 x − 2 y = 2 ⎧ x − 4 y = −1 e) ⎨ ⎩6 x − 3 y = −6 f) ⎧6 x + 7 y = 33 ⎨ ⎩3 x − 3 y = −42 g) ⎧⎪ 4 x − 3 y = 30 + x ⎨ ⎪⎩ 4 x = − ( y + 2 ) + 3 x h) ⎧ x − y = −4 ⎪ ⎨1 1 ⎪⎩ 2 x + 2 y = −3 i) ⎧ 4 x + y = 11 ⎨ ⎩12 x + 3 y = 33 j) ⎧−6 x − 24 y = −10 ⎨ ⎩5 x + 20 y = 0 Teaching Notes: • • • • • Remind students to check their solution in the original equations. Many students write their final answer as x = a number and y = a number rather than an ordered pair (x, y). Many students find working with fractional coefficients challenging. Refer students to the textbook’s summary “To Solve a System of Two Linear Equations by the Substitution Method”. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) (3, 6); 1b) (2, 4); 1c) (-4, 1); 1d) (0, -1); 1e) (-1, 0); 1f) (-5, 9) ; 1g) (4, -6); 1h) (-5, -1); 1i) infinite; 1j) no solution.

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