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Algebra - Two Variables

Variable Substitution

You can solve a system of equations with a method called substitution. Hereâ€™s how to use it.

You have two equations, so â€œsolveâ€ one equation by writing A in terms of B. That is, use the
rules of algebra to rearrange the equation to get â€œA =â€ on one side. Then substitute this
expression into the other equation wherever variable A appears. This results in one equation
and one unknown.

Example:

y = 4x

x + y = 90

What are the values of x and y?

Solution:

The first equation y
= 4x tells you that â€œ4xâ€ is another name for y.

Substitute 4x for y:

x + y = 90

x + 4x = 90

5x = 90

Divide both sides by 5:

5x/5 = 90/5

x = 18

To find y, substitute 18 for x in either
of the original equations:

y = 4x

y = 4(18)

y = 72

Substitute the values of x and y into
the other equation: