Modelling with Linear Relationships
Solving simultaneous equations: Solution by elimination (Cycling puzzle part 4)

Modelling with Linear Relationships

Linear Algebra Skills

• Finding the gradient between coordinates
• Graphing linear equations (slope-intercept form)
• Graphing linear equations (general form)
• Vertical and horizontal lines
• Finding equations of linear graphs in slope-intercept form (part 1)
• Finding equations of linear graphs in slope-intercept form (part 2)
• Finding equations of linear graphs in general form

Solving Simultaneous Equations (Cycling Puzzle Series)

• Introduction (Cycling Puzzle Part 1)
• Graphical solution (Cycling Puzzle Part 2)
• Solution by substitution (Cycling Puzzle Part 3)
• ​Solution by elimination (Cycling Puzzle Part 4)​

The Feasible Region (Fete Stall Series)

• Introduction (Fete Stall Part 1)
• Graphing the feasible region (Fete Stall Part 2)​
• Defining the feasible region (Fete Stall Part 3)
• Setting up additional constraints (Fete Stall Part 4)

​​Linear Programming Skills

• Constructing constraints
• Graphing constraints
• Finding the optimal solution
• Considering Wastage
• Dealing with Discrete Only Solutions

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.