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Solving Systems of Linear Equations by Graphing, Study notes of Calculus

University of Northwestern Ohio (UNOH)Calculus

Lessons on how to solve systems of linear equations by graphing. It includes examples of solving systems with two and more equations, real-world problem solving, interpreting solutions, systems with no solution, and systems with infinitely many solutions.

Typology: Study notes

2021/2022

Uploaded on 09/27/2022

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7-1:%%SOLVING%SYSTEMS%BY%GRAPHING%

Lesson&Objectives:&

• Solve&systems&by&graphing&

• Analyze&special&types&of&systems&

Two!or!more!linear!equations!together!form!a!system%of%linear%equations.!!One!way!to!solve!a!system!of!

linear!equations!is!by!graphing!each!equation.!!Look!for!any!point!common!to!all!the!lines.!!Any!ordered!

pair!in!a!system!that!makes!all!the!equations!true!is!a!solution%of%the%system%of%linear%equations.!

EXAMPLE'1:'''SOLVING'A'SYSTEM'OF'EQUATIONS&

1. Solve!by!graphing.!

y!=!2x!-3!

y!=!x!-!1!

Solve!by!graphing.!

2.!!y!=!4x!-!2! ! ! 3.!!y!=!3x!+!2!

!!!!!y!=!-3x!+!5! ! ! !!!!2x!+!y!=!-8!

Discover Study notes of Calculus University of Northwestern Ohio (UNOH)

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Download Solving Systems of Linear Equations by Graphing and more Study notes Calculus in PDF only on Docsity!

7 - 1 : SOLVING SYSTEMS BY GRAPHING

Lesson Objectives:

• Solve systems by graphing

• Analyze special types of systems

Two or more linear equations together form a system of linear equations. One way to solve a system of

linear equations is by graphing each equation. Look for any point common to all the lines. Any ordered

pair in a system that makes all the equations true is a solution of the system of linear equations.

EXAMPLE 1: SOLVING A SYSTEM OF EQUATIONS

1. Solve by graphing.

y = 2x - 3

y = x - 1

Solve by graphing.

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

y = - 3x + 5 2x + y = - 8

EXAMPLE 2: REAL-WORLD PROBLEM SOLVING

4. Suppose you are testing two fertilizers on bamboo plants A and B, which are growing under identical

conditions. Plant A is 6 cm tall and growing at a rate of 4 cm/day. Plant B is 10 cm tall and growing at a

rate of 2 cm/day. Write a system of equations that models the height of each plant H(d) as a function of

days d.

EXAMPLE 3: INTERPRETING SOLUTIONS

5. Find the solution to the system in #4. What does the solution mean in terms of the original situation?

6. Two friends are walking around a quarter-mile track. One person has completed six laps before the

second one starts. The system below models the distance d(t) in miles each walker covers as a function

of time t in hours.

d(t) = 3t + 1.5 d(t) = 4t

a) Find the solution of the system by graphing. (Hint: use units of 0.5 on your graph)

b) What does the solution mean in terms of the original situation?

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Solve each system by graphing.

42 − 10 x = 7 y − 49 = − 3 x + 7 y

x

y

− 6 x + 25 = − 5 y 0 = − 3 + 3 y

x

y

1 + 7 x = − y y − x = − 9

x

y

− 32 x = − 18 y + 162 2 3 x = 2 y + 8

x

y

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