Simultaneous Equations
Cycling Puzzle Solution By Elimination

Simultaneous Equations

Solving linear equations {revision}

• Solving basic linear equations
• Solving more complex linear equations
• Unknowns on both sides

Solving rational equations

• Solving rational equations (part 1)
• Solving rational equations (part 2)
• Solving rational equations (part 3)

Linear inequalities

• Solving linear inequalities​

Graphs of linear equations

• Finding the gradient
• Perpendicular gradients
• Graphing linear equations (slope-intercept form)
• Graphing linear equations (standard form)

Solving simultaneous equations (bicycle problem)

• Introduction problem
• Graphical solution
• Solution by substitution
• Solution by elimination​

We will now consider some algebraic methods for solving simultaneous equations.
​If both equations are given in general form, then the method of solution by substitution becomes unnecessarily long and tedious. So instead, the method solution by elimination can be used.
In this method, the coefficients of either the x or the y are made the same size. Then depending on the sign of the variable, the equations are either added or subtracted together to eliminate one of the variables.