Practical problems using linear and simultaneous equations
Simultaneous equations are incredibly useful for real life applications. They are used for problems that have at least two unknown quantities and at least two pieces of information involving both of these quantities.
How to solve a real life problem using simultaneous equations:
Read the question entirely from start to finish.
Assign variables to each unknown quantity (for example, let x be the number of \ldots)
Use the information given in the question to develop simultaneous linear equations.
Use either substitution, elimination or graphical methods to find solution to simultaneous equations.
Answer the problem given in the question.
Examples
Example 1
The length of a rectangle is 12 units more than the width, and the perimeter of the rectangle is 56 units. Let y be the width and x be the length of the rectangle.
Use the fact that the length of the rectangle is 12 units more than the width to set up an equation for x and y.
Use the fact that the perimeter of the rectangle is 56 units to set up an another equation for x and y.
First solve for y to find the width.
Now solve for x to find the length
How to solve a real life problem using simultaneous equations:
Read the question entirely from start to finish.
Assign variables to each unknown quantity (for example, let x be the number of \ldots)
Use the information given in the question to develop simultaneous linear equations.
Use either substitution, elimination or graphical methods to find solution to simultaneous equations.
Answer the problem given in the question.