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Both calculators run independently — change the inputs on either side to compare results.

2x2 Linear System Solver

Solve a system of two linear equations (ax + by = e and cx + dy = f) instantly. Use it when you need exact values of x and y that satisfy both equations simultaneously.

a (ax + by = e)

c (cx + dy = f)

Fill in the required fields to see your result.

Linear Algebra

Quadratic Form Calculator

Evaluate a 2-variable quadratic form Q(x₁, x₂) and analyze its definiteness. Useful in optimization, geometry, and studying conic sections.

Coefficient a₁₁

Coefficient a₁₂

Coefficient a₂₂

Variable x₁ value

Variable x₂ value

Fill in the required fields to see your result.

Key differences

	2x2 Linear System Solver	Quadratic Form Calculator
Category	Linear Algebra	Linear Algebra
Inputs required	6	5
Result	Solution for x	Quadratic Form Value
What it does	Solve a system of two linear equations (ax + by = e and cx + dy = f) instantly. Use it when you need exact values of x and y that satisfy both equations simultaneously.	Evaluate a 2-variable quadratic form Q(x₁, x₂) and analyze its definiteness. Useful in optimization, geometry, and studying conic sections.