Application of two simultaneous linear equations. This is linear algebra.
| Materials | Let X = Table requirement | Let Y = Chair requirement | Available inventory |
| Metal | 1 | 2 | 6000 |
| Wood | 3 | 1 | 9000 |
Metal row: Each table uses 1 metal set, each chair uses 2 metal set, and the total available is 6000.
Wood row: Each table uses 3 wood set, each chair uses 1 wood set, and the total available is 9000.
A furniture company manufactures tables and chairs using common components of metal and wood.
To assemble one table, an employee requires 1 metal component set and 3 wood component sets.
To assemble one chair, an employee requires 2 metal component sets and 1 wood component set.
The available material inventory in the stockroom is as follows:
• Metal component sets: 6,000
• Wood component sets: 9,000
| Let X = Table Product | Let Y = Chair Product | Material Inventory Available |
X +
Y =
Equation 1 is the metal constraint. It is telling you how to compute the total metal component needed using the available metal inventory of 6000.
X +
Y =
Equation 2 is the wood constraint. It is telling you how to compute the total wood component needed using the available wood inventory of 9000.
Answer, X , Tables =
Answer, Y, Chairs =
System of Equations: Solved by Microsoft Copilot.
1X + 2Y = 6000 (Metal constraint)
3X + 1Y = 9000 (Wood constraint)
Step 1: Express X in terms of Y
X = 6000 - 2Y
Step 2: Substitute into Equation 2
3(6000 - 2Y) + Y = 9000
18000 - 6Y + Y = 9000
18000 - 5Y = 9000
Step 3: Solve for Y
-5Y = -9000 → Y = 1800
Step 4: Solve for X
X = 6000 - 2(1800) = 2400
✅ Final Answer:
Tables (X) = 2400
Chairs (Y) = 1800
Step 5: Verification
Metal: 1(2400) + 2(1800) = 6000 ✔
Wood: 3(2400) + 1(1800) = 9000 ✔
You can use your handwriting to write the equation using Microsoft Math Solver. Actual routine calculation is now easy. But you still need to learn how to write the correct algebraic equations.
IMPORTANT to enter 1 if there is no constant on X and Y. Since 1 * X = X and 1 * Y = Y.
The Two simultaneous linear equation can be solved manually using
determinant of matrix 2x2 and Cramer's procedure. Because it is time consuming to solve this type of problem by hand calculation , calculator or computer program was created to help us to solve similar problem quickly.
Material
let X = Table
let Y = Chair
Inventory
Metal components
1 X +
2 Y =
6000
Wood components
3 X +
1 Y =
9000
X - represent number of table assembled = 2400
Y - represent number of chair assembled =1800
Customer order 3000 tables - 2400 available = 600 balance
Customer order 2000 chairs - 1800 available = 200 balance
Buy Metal components
1 x 600 more table
2 x 200 more chair
600 + 400 = 1000
Buy Wood components
3 x 600 more table
1 x 200 more chair
1,800 + 200 = 2000
Total metal component
6000 inventory + 1000 new order =7,000
Total wood component
9000 inventory + 2000 new order = 11,000
How do you know if your answer is correct and valid? Simply substitute the value of X and Y in equation 1 and equation 2. If you substitute the total metal component = 7000 instead of 6000 and total wood component = 11000 instead of 9000. You will get the required quantities ordered 3000 for tables and 2000 for chairs.
Now student and teacher will no longer need to check the test exam paper because it is done automatically. This will save teacher a lot of time in checking paper.
Learning algebra is important for solving many linear equation problems. It is a very important skill that every student must master. Why? Because algebra gives students the training and stamina to persevere, to formulate ideas, and to grapple with complex problems. It trains students to reflect on their thinking during the problem-solving process and to develop habits of persistence. It also teaches them to gather proof and evidence for critical analysis. In algebra, students are trained to analyze a problem situation, determine the question(s) to be answered, organize the given information, and decide how to represent the problem.
Today, with machine learning and artificial intelligence, the hard part of performing actual computations has become easy—as you can see from using this software tool. But the concept of algebra remains the same. Algebra connects the quantitative relationships of physical things, like the number of tables and chairs you want to solve for. It deals with representing physical objects as letter variables—for example, let the letter X represent the number of tables, and Y represent the number of chairs.
Now, the teacher's job is to help students realize that every letter or variable in an algebraic equation represents a physical object. Teachers try to convince their students that algebra is a cool tool—because when they solve algebraic equations, it's like playing with physical materials in a laboratory, but without spending money on actual materials. It’s all done with paper and pencil or through computer simulations.
Algebra is widely used in computer simulation modeling. When students eventually work with real-world materials, their skills in algebra will save them both time and money.
Graphical solution of two linear equations problem
converge or intersect or common point meaning single solution
Graphical solution of two linear equations problem, two line equations overlap with each other meaning infinite solution. This overlapping happens when you multiply line equation 1 by any number. In this example multiplied by 2
Graphical solution of two linear equations problem, two line equations parallel with each other meaning they will never intersect therefore there is no solution common to both line equation. This parallel circumstances happens when the constant value of "x" also called the slope, represented by variable letter m in line slope equation y = mx + b are both equal. In this example the constant value of x = 1.5 or the slope m = 1.5
IN-V-BAT-AI helps you recall information on demand—even when daily worries block your memory. It organizes your knowledge to make retrieval and application easier. 🔗
Source: How People Learn II: Learners, Contexts, and Cultures
Copyright 2025
Never Forget with IN-V-BAT-AI
INVenting Brain
Assistant Tools
using Artificial Intelligence
(IN-V-BAT-AI)
Since
April 27, 2009
April 27, 2009