Systems of equations

Summary

• A system of two linear equations in two unknowns can be written as

\[ax+by=c\]

\[dx+ey=f\]

• where \(x,y\) are variables and \(a,b,c,d,e,f\) are constants.
• The linear system can have no solution, exactly one solution or an infinite number of solutions.
• Two primary methods of solving the system:
• Method of substitution : Solve one of the equations for one of the variables in terms of the other and substitute the solution into the other equation.
• Method of elimination : Multiply one equation by a non-zero constant and add to the other equation to eliminate one variable.