Linear Equation Solver Calculator
body {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f8f9fa;
color: #333;
line-height: 1.6;
margin: 0;
padding: 20px;
}
.calculator-container {
max-width: 700px;
margin: 40px auto;
background-color: #ffffff;
padding: 30px;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1);
display: flex;
flex-wrap: wrap;
gap: 30px;
}
.calculator-header {
width: 100%;
text-align: center;
margin-bottom: 20px;
border-bottom: 1px solid #eee;
padding-bottom: 15px;
}
.calculator-header h2 {
color: #004a99;
margin: 0;
}
.inputs-section {
flex: 1;
min-width: 280px;
}
.input-group {
margin-bottom: 20px;
text-align: left;
}
.input-group label {
display: block;
margin-bottom: 8px;
font-weight: 600;
color: #555;
}
.input-group input[type="number"],
.input-group input[type="text"] {
width: calc(100% – 20px);
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
box-sizing: border-box;
font-size: 1rem;
}
.input-group input[type="number"]:focus,
.input-group input[type="text"]:focus {
border-color: #004a99;
outline: none;
box-shadow: 0 0 0 2px rgba(0, 74, 153, 0.2);
}
.button-group {
width: 100%;
text-align: center;
margin-top: 25px;
}
.button-group button {
background-color: #004a99;
color: white;
border: none;
padding: 12px 25px;
border-radius: 5px;
font-size: 1.1rem;
cursor: pointer;
transition: background-color 0.3s ease;
font-weight: 600;
}
.button-group button:hover {
background-color: #003366;
}
.results-section {
flex: 1;
min-width: 280px;
background-color: #e9ecef;
padding: 20px;
border-radius: 5px;
text-align: center;
display: flex;
flex-direction: column;
justify-content: center;
align-items: center;
}
#result, #message {
font-size: 1.8rem;
font-weight: bold;
color: #004a99;
margin-top: 10px;
word-wrap: break-word;
}
#message.error {
color: #dc3545;
font-size: 1.1rem;
}
#result.success {
color: #28a745;
}
.explanation-container {
max-width: 700px;
margin: 40px auto;
background-color: #ffffff;
padding: 30px;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1);
}
.explanation-container h3 {
color: #004a99;
border-bottom: 2px solid #004a99;
padding-bottom: 10px;
margin-bottom: 20px;
}
.explanation-container p, .explanation-container ul {
margin-bottom: 20px;
}
.explanation-container code {
background-color: #e9ecef;
padding: 2px 6px;
border-radius: 3px;
font-family: Consolas, Monaco, 'Andale Mono', 'Ubuntu Mono', monospace;
}
@media (max-width: 600px) {
.calculator-container {
flex-direction: column;
padding: 20px;
}
.inputs-section, .results-section {
min-width: 100%;
}
.results-section {
margin-top: 20px;
}
}
Understanding Linear Equations and How to Solve Them
A linear equation in one variable, typically represented in the form ax + b = c, is a fundamental concept in algebra. Here:
x is the variable we want to solve for.a is the coefficient of the variable x. It's the number multiplied by x.b is a constant term on the same side as the variable term.c is a constant term on the other side of the equation.
The goal of solving a linear equation is to isolate the variable x, finding the specific value that makes the equation true. This calculator helps you find that value quickly and accurately for equations of the form ax + b = c.
How the Calculator Works
The calculator applies algebraic principles to rearrange the equation and find the value of x. The steps are as follows:
- Isolate the variable term: Subtract the constant
b from both sides of the equation. This gives us ax = c - b.
- Solve for the variable: If the coefficient
a is not zero, divide both sides by a. This yields x = (c - b) / a.
Special Cases
- If a = 0 and (c – b) = 0: The equation becomes
0x + b = c, which simplifies to 0 = 0 (since b=c). This means the equation is true for ALL values of x. It's an identity.
- If a = 0 and (c – b) ≠ 0: The equation becomes
0x + b = c, which simplifies to 0 = (c - b). Since c - b is not zero, this statement is false. There is NO solution for x that can satisfy this equation.
Use Cases for Linear Equation Solvers
Linear equations are foundational in mathematics and appear in numerous real-world applications:
- Physics: Calculating motion, forces, and energy often involves linear relationships.
- Economics: Modeling supply and demand, cost functions, and break-even points.
- Engineering: Designing circuits, analyzing structures, and controlling systems.
- Computer Science: Algorithms and data analysis frequently utilize linear equations.
- Everyday Budgeting: Calculating how much of a certain item you can afford based on price and total budget.
Example Calculation
Let's solve the equation 3x + 5 = 14:
- Here,
a = 3, b = 5, and c = 14.
- Step 1: Subtract
b from both sides: 3x = 14 - 5 which simplifies to 3x = 9.
- Step 2: Divide by
a: x = 9 / 3.
- Result:
x = 3.
Enter 3 for 'a', 5 for 'b', and 14 for 'c' into the calculator above to verify this result.
function solveLinearEquation() {
var a = parseFloat(document.getElementById("coefficientA").value);
var b = parseFloat(document.getElementById("constantB").value);
var c = parseFloat(document.getElementById("constantC").value);
var resultDiv = document.getElementById("result");
var messageDiv = document.getElementById("message");
resultDiv.textContent = "";
resultDiv.className = ""; // Reset classes
messageDiv.textContent = "";
messageDiv.className = ""; // Reset classes
// Check if inputs are valid numbers
if (isNaN(a) || isNaN(b) || isNaN(c)) {
messageDiv.textContent = "Please enter valid numbers for all coefficients.";
messageDiv.className = "error";
return;
}
// Equation is ax + b = c
if (a === 0) {
// Case 1: a is 0
var difference = c – b;
if (difference === 0) {
// 0x + b = c becomes 0 = 0 (since b=c)
messageDiv.textContent = "Infinite Solutions";
messageDiv.className = "error"; // Often treated as an exceptional case
resultDiv.textContent = "All real numbers";
resultDiv.className = "success";
} else {
// 0x + b = c becomes 0 = (c – b) which is false
messageDiv.textContent = "No Solution";
messageDiv.className = "error";
resultDiv.textContent = "Contradiction";
}
} else {
// Case 2: a is not 0
// ax = c – b
// x = (c – b) / a
var x = (c – b) / a;
resultDiv.textContent = "x = " + x.toFixed(4); // Display with 4 decimal places
resultDiv.className = "success";
}
}