Lesson 13: Simultaneous Linear Equations: Solving Word Problems (II)

March 5, 2011

3. Solving word problems with simultaneous linear equations

Systems of linear equations are a powerful tool to solve problems. Many problems lead themselves to being solved with systems of linear equations. In “real life”, these problems can be incredibly complex. This is one reason why linear algebra (the study of linear systems and related concepts) is a very important branch of mathematics. However, you will face with much simpler problems in Secondary Education. Here you are some typical examples.

Steps for Solving Word Problems

 1. Read the problem. Relax. Underline important words and values.

 2. (Read again). Introduce variables:

 Let x = describe in words

Let y = describe in words

3.(Read again). Make a Table:


  Description of x Description of y Total
Description for combined quantities ax     bya’x     b’y cc’
4. Write down the system of equations (from table):
ax + by  = c a’x + b’y = c’

 5.Solve for  x and  y using substitution, equalizing or elimination.

6.Write the answer in words including proper units.

7.Check the answers not only in the system but also in the context of the problem.

Here you are a good site to practise.

First you have got solved examples. At the bottom of the page you will find a generator of problems. But you can jump right to the exercises if you click on the link that says Jump right to the exercises! at the beginning.

  1. Click on “new problem” to get started.
  2. On these exercises, you will not key in your answer.
  3. However, you can check to see if your answer is correct on answer. The solution is explained in detail.

Finally here you are a video where is explained how to solve a numeric word problem with simultaneous linear equations.


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