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数学

Algebraic Equation Solver – Step-by-Step Logic | CalcTools

Solve linear and quadratic equations with a detailed pedagogical breakdown. Perfect for students and academic reporting.

Understanding algebra is not just about finding the answer; it's about mastering the logical steps required to isolate a variable. Our Step-by-Step Equation Solver is designed as a pedagogical companion for students and researchers. It takes your algebraic input and provides a transparent derivation path, showing exactly how the equation is standardized, simplified, and solved. Whether you're dealing with basic linear relationships or more complex identities, this tool ensures you understand the 'why' behind every 'x'.
Systems (Ax=B)
Derivatives (d/dx)
Integrals (∫)
Polynomials

Academic Report

System of 2 Linear Equations

Matrix Setup (Ax = B)
[211−1][xy]=[104]\begin{bmatrix} 2 & 1 \\ 1 & -1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 10 \\ 4 \end{bmatrix}

Convert the system of linear equations into Matrix notation.

Determinant Analysis
det⁡(A)=−3\det(A) = -3

Determinant is non-zero. A unique solution exists.

Final Solution

x=4.667,y=0.6667x = 4.667, \quad y = 0.6667
Quick Start
Universal Engine

This engine automatically detects linear systems, polynomial roots, and calculus operations based on your input syntax.

使い方

This tool uses a symbolic algebraic engine to parse your equation. It first standardizes the expression by moving all terms to one side, then applies simplification rules to combine like terms, and finally identifies the roots using derivation logic.

計算式

Zero Identity Path: f(x) = g(x) \to f(x) - g(x) = 0

Calculation Examples

1. **Linear**: 2x + 5 = 15 shows the subtraction and division steps. 2. **Algebraic**: x^2 - 9 = 0 demonstrates isolation using roots.

Why use this tool in your daily life?

This is your personal math tutor. By revealing the hidden mechanics of algebraic manipulation, it helps bridge the gap between abstract formulas and concrete solutions, providing professional-grade reports for your academic work.

ヒント

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関連ツール

Standard Calculator – Fast & Reliable Basic Math | CalcTools
Perform basic arithmetic operations including addition, subtraction, multiplication, and division. A modern, responsive tool for daily calculations.
関数電卓
三角関数、対数、累乗を含む、高度な数学のためのフル機能の関数電卓。
関数グラフ作成
インタラクティブな2Dグラフ電卓。一次、二次、三角関数などの数学関数を可視化します。
二次方程式解法
二次方程式を即座に解きます。実数解および虚数解を求めます。
平方根計算機
任意の正の数値の平方根を素早く求めます。
平均・中央値・最頻値
数値セットの平均（算術平均）、中央値、最頻値を計算します。

その他の数学ツール

Standard Calculator – Fast & Reliable Basic Math | CalcTools

開く

Perform basic arithmetic operations including addition, subtraction, multiplication, and division. A modern, responsive tool for daily calculations.

関数電卓

開く

三角関数、対数、累乗を含む、高度な数学のためのフル機能の関数電卓。

関数グラフ作成

開く

インタラクティブな2Dグラフ電卓。一次、二次、三角関数などの数学関数を可視化します。