Substiution Method

In the substitution method, how do you know which variable to begin with?

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Apr 24, 2010
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by: Karin

When using the substitution method, you can solve any equation for a variable (if necessary).

Here's a few examples:

Example 1:
x + y = 5
y = -4x

In this system, the 2nd equation (y = -4x) is already solved for y. It begins with y = ... Therefore, I can substitute -4x for y in the 1st equation to begin the solving process. (This system is already set up for solving)

Example 2:
2x + y = 3
3x - 5y = 8

This system is not set up for the substitution method. I need to choose one of the equations and solve for a variable.

I would choose the 1st equation because the variable y is easy to solve for since it does not have a coefficient.

2x + y = 3
2x -2x + y = 3 - 2x
y = -2x + 3

Now the first equation is solved for y and I can substitute -2x + 3 for y into the 2nd equation.


Example 3:
5x + 2y = -10
x - 3y = -2

This system is not set up for using the substitution method either. I need to choose one equation and solve for a variable.

I would choose equation #2 (x - 3y = -2) because x does not have a coefficient, so it is easy to solve for x.

x - 3y = -2
x - 3y +3y = -3 + 3y
x = 3y - 3

Now we can substitute 3y - 3 for x into the 1st equation.

You can choose to solve for either variable in either equation to get set up. Look for a variable that does not have a coefficient (It's actually a coefficient of 1, but we don't write it).

I hope this helps you in your studies.

Karin

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