Algebra
Advanced

System of Two Linear Equations

Cramer-rule solution for two simultaneous equations.

Formula

x=c1b2−c2b1a1b2−a2b1x = \frac{c_1 b_2 - c_2 b_1}{a_1 b_2 - a_2 b_1}

Variables

a,b,cEquation coefficients

Example

Solves a₁x+b₁y=c₁ pair

Did You Know?

Simultaneous equations were solved in ancient China using counting rods in a method essentially identical to modern matrices.

linearsystem