Math
System of Equations Calculator
Use this system of equations calculator for two linear equations in x and y when you need the intersection point.
Solution
—
- x
- —
- y
- —
- Determinant
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the system of equations calculator solves
Use this system of equations calculator for two linear equations in x and y when you need the intersection point.
Formula
How to use it
- Enter each equation in ax + by = c form.
- Check the determinant.
- Read x and y as the intersection point.
How to read the answer
One unique solution means the two lines cross at exactly one point.
Common mistakes and edge cases
- Move constants to the right side before entering.
- A zero determinant means no unique solution.
- Keep coefficient signs exactly as written.
Worked examples
Unique solution
Solution
x = 3.2, y = 2.2
Parallel lines
Solution
No unique solution
Frequently asked questions
What does no unique solution mean?+
It means the lines are parallel with no intersection or are the same line with infinitely many solutions.
Can this solve three equations?+
This page solves 2x2 systems. A 3x3 mode would use the same determinant idea with more equations.
Related calculators
Slope Calculator
Find slope from two points or solve a missing coordinate from a known slope. Includes equations, intercepts, grade, graph, and step-by-step work.
Quadratic Formula Calculator
Solve ax^2 + bx + c = 0 with the quadratic formula, discriminant, roots, and vertex values.
Proportion Calculator
Solve a missing value in a proportion using cross multiplication with clear substitution steps.
Discount Calculator
Calculate sale price, stacked discounts, original price before a discount, or the discount percent between two prices.
Fraction Calculator
Add, subtract, multiply, divide, simplify, compare, or convert decimals to fractions with steps and visual fraction bars.
Percentage Calculator
Calculate percent of a number, part-to-whole percentages, percent change, missing wholes, and reverse percent changes.
Last updated: May 8, 2026