Simultaneous Equations

Rules for Simultaneous Equations

• Understand that simultaneous equations are a set of equations with multiple variables that are solved together. Each equation provides additional information needed to find the solution.
• Be aware that there can be two types of simultaneous equations: linear-linear type and quadratic-linear type.
• Remember that linear-linear type simultaneous equations can be solved by substitution, elimination or comparison.
• Note that the quadratic-linear type can be dealt with by substitution, where the solution of one equation is substituted into another to help solve for one or both variables.

Solving Linear-Linear Type

• Solve one of the equations for one of its variables. This will allow you to substitute the solution into the other equation.
• Substitute the solved part into the other equation and solve for the second variable.
• Substitute this value into one of the original equations and solve for the other variable.
• Check your solution by substiting both variables into both original equations to ensure they make both equations true.

Solving Quadratic-Linear Type

• If dealing with quadratic-linear simultaneous equations, solve the linear equation for one of the variables
• Substitute the solution of the linear equation from the first point into the quadratic equation then solve.
• Substitute the value you’ve found into the linear equation to find the value of the other variable.
• Always do a double-check to make sure you have the right solution
• Both solutions found are the solutions to the entire system of simultaneous equations.