Learn Before
Problem-Solving Strategy for Systems of Linear Equations
When solving real-world word problems that involve systems of linear equations, the general seven-step problem-solving strategy used for single-equation word problems is adapted so that the Translate step produces a system of equations rather than a single equation, and the Solve step uses a system-solving technique (such as graphing, substitution, or elimination) rather than standard one-variable algebra. The steps are:
- Read the problem. Make sure all the words and ideas are understood.
- Identify what you are looking for.
- Name what you are looking for. Choose variables to represent those quantities.
- Translate the problem into a system of equations.
- Solve the system of equations using good algebra techniques.
- Check the answer in the problem and make sure it makes sense.
- Answer the question with a complete sentence.
The key adaptation is in Steps 3, 4, and 5. Because systems problems typically involve two unknown quantities, Step 3 assigns a separate variable to each unknown. Step 4 then produces two equations — one for each relationship described in the problem — forming a system. Step 5 solves this system using whichever technique is appropriate, such as graphing, substitution, or elimination. Some application problems translate directly into equations in standard form, making the elimination method especially convenient for those cases.
An additional benefit of the systems approach is that some people find setting up word problems with two variables easier than with just one variable — choosing variable names is simpler when each unknown gets its own letter, rather than having to express all quantities through a single variable.
0
1
Tags
OpenStax
Elementary Algebra @ OpenStax
Ch.5 Systems of Linear Equations - Elementary Algebra @ OpenStax
Algebra
Math
Prealgebra
Related
Example: Solving a Word Problem for a Car's Sticker Price
Solving a Word Problem for the Cost Per Pound of Grapes
Solving a Word Problem for a Car's Original Price
Strategy for Solving Formula-Based Applications
Solving a Word Problem for the Number of Boys in a Study Group
Number Problems
Expressing Multiple Unknowns in Terms of a Single Variable
Solving a Combined-Earnings Word Problem Using 'Less Than Twice'
Solving a Tip Calculation Using a Percent Equation
Finding the Total Recommended Daily Amount of Potassium
Finding the Percent of Calories from Fat
Mixture Problems
Problem-Solving Strategy for Systems of Linear Equations
Discarding Unrealistic Negative Solutions in Applications
A retail manager is calculating the necessary markup for a new product line to meet a specific profit goal. To solve this word problem using the standard seven-step algebraic strategy, arrange the first four steps in the correct chronological order.
A project manager is training a new hire on the company's standard seven-step algebraic strategy for solving budget-related word problems. Match each step of the strategy with its correct description to ensure the team follows a consistent process.
A payroll specialist is using the standard seven-step problem-solving strategy to determine a staff member's total overtime compensation. After solving the algebraic equation, the specialist must perform the 'Check' step. What is the primary objective of this step?
Finalizing the Algebraic Problem-Solving Process
A project manager is using the standard seven-step problem-solving strategy to calculate the total budget for a new initiative. True or False: The 'Identify' step of this strategy involves choosing a specific variable, such as 'x', to represent the unknown budget amount.
Recruitment Budget Analysis
A logistics coordinator is following a seven-step strategy to calculate the total number of shipping containers needed for a large export order. After choosing a variable to represent the unknown quantity, the coordinator converts the written requirements of the problem into a mathematical equation. This fourth step in the problem-solving strategy is the ____ step.
Standardizing the Problem-Solving Workflow
A procurement officer is using the standard seven-step algebraic strategy to determine the unit cost of a large supply order. In the third step of this process, known as 'Name', what specific action is required?
A training coordinator is using a standard seven-step strategy to calculate the number of workshops needed for a department expansion. After successfully translating the word problem into a mathematical equation, what is the next step the coordinator must perform according to this strategy?
Solving for Two Consecutive Odd Integers Whose Product is
Solving for Two Consecutive Odd Integers Whose Product is
Solving for Two Consecutive Odd Integers Whose Product is
Example: Solving a Word Problem about Snowfall
Example: Solving a Word Problem about Books
Example: Solving a Word Problem about Puzzles
Learn After
Solving a Two-Number Word Problem Using a System of Equations by Substitution
Solving a Rectangle Perimeter Problem Using a System of Equations by Substitution
Solving a Right Triangle Angle Problem Using a System of Equations by Substitution
Solving a Salary Comparison Word Problem Using a System of Equations by Substitution
Solving a Two-Number Sum and Difference Word Problem Using a System of Equations by Elimination
Solving a Calorie-Counting Word Problem Using a System of Equations by Elimination
Translating a Two-Number Word Problem into a System of Equations
Translating a Combined-Earnings Word Problem into a System of Equations
Solving an Age Word Problem Using a System of Equations by Substitution
Solving an Exercise Calorie Word Problem Using a System of Equations by Elimination
Solving a Three-Sided Fencing Problem Using a System of Equations by Substitution
Solving a Catch-Up Motion Problem Using a System of Equations by Substitution
A project manager is calculating the number of junior and senior consultants needed for a new contract. To find the solution using a system of linear equations, they follow a standard seven-step strategy. Arrange the following key phases of that strategy in the correct chronological order.
A department manager is using the seven-step problem-solving strategy to calculate the costs of two different office supply packages. According to this strategy, which step involves converting the written descriptions of the package costs into a system of equations?
An inventory manager is following a seven-step strategy to determine the quantity of two different products needed for a promotion. Match each of the following steps of that strategy with the specific task required when solving the problem as a system of linear equations.
An inventory specialist is using the seven-step problem-solving strategy to determine the number of laptops and tablets to order for a new department. After solving the system of equations, the specialist must ____ the answer in the original problem to ensure the results make sense and satisfy the department's budget and quantity requirements.
A human resources coordinator is using the seven-step problem-solving strategy to determine the number of part-time and full-time employees needed for a department. True or False: According to this strategy, in Step 3 (Name), the coordinator should assign a separate variable to each of these two unknown quantities.
Algebraic Techniques in the Seven-Step Strategy
Methodology for Solving Procurement Systems
Facility Procurement at Zenith Offices
A project coordinator is using a seven-step problem-solving strategy to determine the number of full-time and part-time staff needed for a new contract. After the coordinator has solved the system of equations and verified that the results are correct, what is the final step they must take according to this strategy?
A warehouse supervisor is using the seven-step problem-solving strategy to determine the number of standard pallets and oversized pallets currently in stock. According to this strategy, which of the following best describes the 'Identify' step?
Solving a Complementary Angle Problem Using a System of Equations by Elimination
Solving a Supplementary Angle Problem Using a System of Equations by Substitution