Simultaneous (Linear) Equations — Formula Sheet

ax+by+c=0

x=3, y=5 satisfy 2x-y=1 and 3x+y=14

Method of elimination by substitution

Method of elimination by equating coefficients

Method of cross-multiplication

x=\frac{b_{1} c_{2}-b_{2} c_{1}}{a_{1} b_{2}-a_{2} b_{1}}

y=\frac{c_{1} a_{2}-c_{2} a_{1}}{a_{1} b_{2}-a_{2} b_{1}}

\frac{x}{b_{1} c_{2}-b_{2} c_{1}}=\frac{y}{c_{1} a_{2}-c_{2} a_{1}}=\frac{1}{a_{1} b_{2}-a_{2} b_{1}}

First write both equations in the form a1x+b1y+c1=0 and a2x+b2y+c2=0.