Math
Linear equation
Solve a one-variable linear equation in the form ax + b = c.
Calculators / Math / Two-equation linear system
Two-equation linear system calculator
Solve two linear equations in x and y using determinants.
On this page
Determinant-5
x3.2
y2.2
Calculator controls
How to calculate
Solve two linear equations in x and y using determinants.
D = ad − bc; x = (ed − bf)/D; y = (af − ec)/D
Worked example
a in ax + by = e: 2; b in ax + by = e: 3; e in ax + by = e: 13; c in cx + dy = f: 1; d in cx + dy = f: -1; f in cx + dy = f: 1.
Determinant: -5 ; x: 3.2 ; y: 2.2 .
Assumptions and limits
A zero determinant means this formula cannot identify one unique solution; the equations may be dependent or inconsistent.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Solve two linear equations in x and y using determinants. Every assumption remains visible so the result can be checked or changed.
When this tool is useful
Use the two-equation linear system for an initial estimate, comparison, or classroom calculation.
Understanding your inputs
| Input | What to enter |
|---|---|
| a in ax + by = e | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| b in ax + by = e | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| e in ax + by = e | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| c in cx + dy = f | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| d in cx + dy = f | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| f in cx + dy = f | Enter a number of at least -1000000000000 and no more than 1000000000000. |
Frequently asked questions
What are the limits of this two-equation linear system?
A zero determinant means this formula cannot identify one unique solution; the equations may be dependent or inconsistent.
Can I use different units?
Use the units printed beside each field. Convert measurements first when your source uses different units.