x+y Linear Equation Solver

Single Equation: ax + b = 0

x =

System: a₁x + b₁y = c₁  &  a₂x + b₂y = c₂

Solution

Solving Linear Equations

A linear equation is an equation where the highest power of the variable is 1. It graphs as a straight line.

Single: ax + b = 0 → x = −b/a
System: solve using substitution or Cramer's rule

Cramer's Rule for 2×2 Systems

x = (c₁b₂ − c₂b₁) / (a₁b₂ − a₂b₁)
y = (a₁c₂ − a₂c₁) / (a₁b₂ − a₂b₁)

Frequently Asked Questions

How do you solve 3x + 12 = 0? ▼
Subtract 12 from both sides: 3x = −12. Divide by 3: x = −4.
What is a system of linear equations? ▼
A system of linear equations is two or more equations with two or more unknowns. The solution is the values of x and y that satisfy ALL equations simultaneously.
What does 'no solution' mean in a linear system? ▼
If the equations are parallel (same slope, different intercepts), there is no point of intersection — hence no solution. If they are the same line, there are infinitely many solutions.