# Systems of equations can be solved by graphing or by using substitution or elimination

Systems of equations can be solved by graphing or by using substitution or elimination. What are the pros and cons of each method? Which method do you like best? Why? What circumstances would cause you to use a different method? Consider some of your responses by indicating pros and cons that you may not have considered or persuading them to see the value of the method you like best (if you chose different methods). Describe situations in which you might use their methods of solving.

© BrainMass Inc. brainmass.com October 16, 2018, 9:29 pm ad1c9bdddfhttps://brainmass.com/math/linear-algebra/comparing-methods-solving-systems-linear-equations-186476

#### Solution Preview

Solve the system: 2x + y = 9, x - y = 3

Elimination / Addition method

This method is preferred when the coefficients of x terms or y terms in the two equations are equal and have opposite signs. If the coefficients are not already equal and negative, it should be easily possible to render them so by multiplying one or both equations with suitable multiplying factor/s.

We see that the coefficients of y terms in the two equations are equal and have opposite ...

#### Solution Summary

This solution shows a comparison between the different methods of solving a system of linear simultaneous equations. As an illustration, one problem has been solved by all the methods: Elimination, Substitution and Graphing. A Word file attachment must be opened to view the solution.

Solving a System by Graphing, substitution & elimination

Problem #20

Solving a System by Graphing

Solve each system by graphing.

y = − 2/3x

2x + 3y =5

Problem # 56

Solving by Substitution

Solve each system by substitution. Determine whether the

equations are independent, dependent, or inconsistent.

2x − y = 4

2x − y = 3

Problem # 70

Solve each system by the substitution method.

x + 3y = 2

− x + y = 1

Problem # 92

Applications

Write a system of two equations in two unknowns for each problem.

Solve each system by substitution.

Investing her bonus. Donna invested her $33,000 bonus

and received a total of $970 in interest after one year. If

part of the money returned 4% and the remainder 2.25%,

then how much did she invest at each rate?

Problem # 30

Solve each system by the addition method. Determine whether

the equations are independent, dependent, or inconsistent.

− 3x + 2y = 8

3x + 2y = 8

Problem # 52

Solve each system by substitution or addition, whichever is easier.

2y − x = 3

x = 3y − 5

Problem # 72

Applications

Write a system of two equations in two unknowns for each

problem. Solve each system by the method of your choice.

Books and magazines. At Gwen's garage sale, all books

were one price, and all magazines were another price.

Harriet bought four books and three magazines for $1.45,

and June bought two books and five magazines for $1.25.

What was the price of a book and what was the price of a

magazine?

Problem # 82

Applications

Write a system of two equations in two unknowns for each

problem. Solve each system by the method of your choice.

Super Bowl contender. The probability that San Francisco

plays in the next Super Bowl is nine times the probability

that they do not play in the next Super Bowl. The probability

that San Francisco plays in the next Super Bowl plus the

probability that they do not play is 1. What is the probability

that San Francisco plays in the next Super Bowl?