📐 System of Equations Calculator
Solve systems of equations
How to Use This Calculator
Choose Method
Select elimination or substitution method
Enter Equations
Type your system of equations
Solve
See the solution steps using your chosen method
Methods
Elimination Method Example:
System: 2x + 3y = 7, x - y = 1
1. Multiply Eq 2 by 3: 3x - 3y = 3
2. Add to Eq 1: 5x = 10
3. Solve: x = 2
4. Substitute: 2 - y = 1 → y = 1
Solution: x = 2, y = 1
Substitution Method Example:
System: y = 2x + 1, x + y = 10
1. Substitute y: x + (2x + 1) = 10
2. Simplify: 3x + 1 = 10
3. Solve: x = 3
4. Substitute: y = 2(3) + 1 = 7
Solution: x = 3, y = 7
About System of Equations Calculator
The System of Equations Calculator solves systems of linear equations using either the elimination method (adding/subtracting equations) or substitution method (solving one equation and substituting into the other). Both methods find the point where the lines intersect.
When to Use Each Method
- Elimination: Good when coefficients are easy to eliminate
- Substitution: Good when one variable is already isolated
Types of Solutions
- One Solution: Lines intersect at one point
- No Solution: Parallel lines (inconsistent system)
- Infinite Solutions: Same line (dependent system)
Frequently Asked Questions
Which method should I use?
Use elimination if coefficients are easy to cancel. Use substitution if one variable is already isolated.
Can I solve 3x3 systems?
Yes! Extend the same methods to systems with three variables and equations.