Home / Math / System of Equations

System of Equations Solver

Solution Found:

Step-by-Step Solution (Elimination):

What is a System of Linear Equations?

A system of linear equations consists of two or more linear equations that share the same variables (usually x and y). Solving the system means finding the specific values for x and y that make both equations true at the same time.

Graphically, this solution represents the exact point where the two lines cross (intersect).

® Formulas & Methods

Equations are typically written in Standard Form:

Ax + By = C

To solve them, we typically use one of three methods: Graphing, Substitution, or Elimination. This calculator uses the Elimination method.

Example Problem:

Equation 1: x + y = 5
Equation 2: x - y = 1

Step 1: Add the two equations together to eliminate 'y':
(x + x) + (y - y) = 5 + 1
2x = 6

Step 2: Solve for x:
x = 3

Step 3: Substitute x back into Equation 1:
3 + y = 5 → y = 2

Answer: (3, 2)

❓ Frequently Asked Questions

1. How do I type equations into this tool? +
Type them exactly as they appear in your math book. You don't need to separate numbers. Examples: 2x+y=10 or x-y=5. Spaces are ignored.
2. What is the Elimination Method? +
The Elimination Method involves multiplying one or both equations by a number so that when you add or subtract them, one variable (like x or y) is cancelled out, allowing you to solve for the other.
3. What does "No Solution" mean? +
It means the two lines are parallel. They have the same slope but different intercepts, so they will never cross. There is no (x, y) pair that satisfies both.
4. What does "Infinite Solutions" mean? +
It means the two equations actually represent the same line. Every point on the line is a solution to the system.
5. Can I use decimals or fractions? +
Yes! You can type decimals like 0.5x + 2.5y = 10. For fractions, convert them to decimals first (e.g., use 0.5 instead of 1/2).