Simultaneous Linear Equations

Simultaneous Linear Equations

Consider two linear equations in two variables, x and y, such as

          2x - 3y = 4

          3x + y = 1

Instead of one equation in one unknown, we have here two equations and two unknowns. In order to find a solution for this pair of equations, the unknown numbers x and y have to satisfy both equations. Hence, we call this system or pair of equations or simultaneous equations. We now focus on various methods of solving simultaneous equations.

Intersection Point of a Line with a Horizontal or Vertical Line

We first consider the special cases of solving a pair of simultaneous linear equations when one of the two lines is either horizontal (ay = b) or vertical (cx = d); the solution in these cases is easily found by substitution.

Example 1A.

Case one: One line is horizontal (ay = b):

Exercise 1A.

Now try solving a few on your own:

Example 1B.

Case two: One line is vertical (cx = d). The method is exactly the same as for a vertical line.

Exercise 1B.

Practice this method with a few exercises:

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