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Chapter 5: Problem 72

When is it easier to use the addition method rather than the substitution method to solve a system of equations?

Short Answer

Expert verified
The addition (or elimination) method for solving a system of equations might be easier to use when the coefficients of one variable are the same or differ only by a sign in the given equations. Whereas, the substitution method tends to be simpler when a variable is already isolated or can be isolated easily in one of the equations.

Step by step solution

01

Understanding the Addition Method

The addition method, also known as elimination method, involves adding or subtracting the given equations to eliminate one of the variables, making it easier to solve for the remaining variable. This method can be particularly useful if the coefficients of a certain variable in both equations are the same or differ only in sign, which allows the variable to be easily eliminated when the equations are added or subtracted.
02

Understanding the Substitution Method

In the substitution method, one of the equations is rearranged to find one variable in terms of the other, and then that expression is substituted into the second equation. This method is often easier if one variable is already isolated in one of the equations, or can easily be isolated with little manipulation.
03

Deciding which Method to Use

The addition method might be simpler if the coefficients of one variable in both equations are identical or only differ by a sign. The substitution method is typically easier if one variable is already isolated in one of the equations or can easily be isolated.

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Most popular questions from this chapter

Describe how to solve a system of inequalities.

Explain how to find the partial fraction decomposition of a rational expression with a prime quadratic factor in the denominator.

In Exercises \(43-46,\) let \(x\) represent one number and let \(y\) represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. The sum of two numbers is \(2 .\) If one number is subtracted from the other, their difference is \(8 .\) Find the numbers.

In Exercises \(1-4,\) determine whether the given ordered pair is a solution of the system. $$ \begin{aligned} &(8,5)\\\ &5 x-4 y=20\\\ &3 y=2 x+1 \end{aligned} $$

In Exercises \(31-42,\) solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. \(9 x-3 y=12\) \(y=3 x-4\)
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