Equation Solver Calculator
Solve linear, quadratic, and system of equations with step-by-step solutions
Equation Solver Calculator
Solve linear equations, quadratic equations, and systems of two linear equations. Enter the coefficients and get detailed step-by-step solutions.
📐 Equation Solver
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📚 Understanding Equations
Linear Equations
A linear equation has the form ax + b = c, where the variable x appears only to the first power. To solve, isolate x by subtracting b from both sides, then dividing by a.
Quadratic Equations
A quadratic equation has the form ax² + bx + c = 0. It can have two, one, or no real solutions, determined by the discriminant (b² - 4ac). The quadratic formula provides exact solutions.
Systems of Equations
A system of two linear equations involves finding values of x and y that satisfy both equations simultaneously. Common methods include substitution, elimination, and Cramer's rule using determinants.
How to Solve Equations
An equation is a mathematical statement that asserts the equality of two expressions. Solving an equation means finding the value(s) of the unknown variable(s) that make the statement true.
Solving Linear Equations
To solve a linear equation like 2x + 3 = 7, follow these steps:
Step 1: Subtract 3 from both sides: 2x = 4
Step 2: Divide both sides by 2: x = 2
Solving Quadratic Equations
Quadratic equations can be solved using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
The discriminant (b² - 4ac) determines the nature of solutions: if positive, two distinct real roots; if zero, one repeated real root; if negative, two complex conjugate roots.
Solving Systems of Equations (Cramer's Rule)
For a system of two equations a₁x + b₁y = c₁ and a₂x + b₂y = c₂, Cramer's rule uses determinants:
D = a₁b₂ - a₂b₁
x = (c₁b₂ - c₂b₁) / D
y = (a₁c₂ - a₂c₁) / D
If D = 0, the system has either infinitely many solutions (dependent equations) or no solution (inconsistent equations).