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Simultaneous Linear Equations

The Substitution Method

This method involves making one variable the subject of an equation, and substituting it into the other equation to obtain an equation with a single variable.

Example 3.

Equation 1:          
x + y =
Equation 2:          
x + y =

Click on the buttons below to see how to solve these equations.

       y = ( )

       x + ( ) =

       x = (2 d.p.)

       y = (2 d.p.)

Here it was easy to first make y the subject of Equation 2, as the coefficient of y is 1. We could still solve the problem in this way even if the coefficient of y was not 1, it would just involve more algebra and possibly fractional coefficients. If Equation 1 had a y coefficient of 1, it would be best to make y the subject of equation 1 and then substitute into Equation 2. Similarly, if x had a coefficient of 1 in either equation, you could rearrange that equation to make x the subject of the equation and the substitute for x in the other equation. To see some examples of these, click the "More" link below.

More Examples (this will open in another window)

Exercise 3.

Now practice with a few of these exercises:

Equation 1:          
x + y =
Equation 2:          
x + y =

Make y the subject of the second equation:

                   y = ( )                          

Substituting your expression for y in the first equation, we obtain:

x + ( ) =              

Solve the above equation for x:

x =

Substitute x in your expression for y and solve for y:

y =

<< The Elimination Method | Simultaneous Linear Equations Index | Geometric or Graphical Interpretation >>

 

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