How to Solve by Substitution

When given simultaneous equations (also known as a system of equations), learning how to solve by substitution is usually the first method that you will learn.  Other methods are graphing and elimination.

The substitution method is easiest to use when one of your equations has a variable that is isolated (solved for).

For a colorful video explaining the process (recommended) click here.

Systems of Equations:            

How to Solve by Substitution

More examples of solving by substitution.

Take both original equation and write them side by side:

	substitute:	y = 4x	x + y = 10
	x = 2, y = 8	8 = 4(2)	2 + 8 = 10
	simplify:	8 = 8	10 = 10
	Check:	√	√

Once you simplify the equations, both sides should be equal to the same number.  In this case, 8 = 8 and 10 = 10, so they both check!

You should now know how to solve by substitution.  However, you do not want to use this method all the time.  In particular, the elimination method is the easiest to use when both of your equations are in the format:

     x + y = #     That is, you have x first, y second - equal to a constant.

Example:  Solve 2x + 3y = 7 and 4x + y = 9 for x and y.

    Notice how both equations have x first, then y, then the constant?

More information on using the elimination method.

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