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**Solving Simultaneous Equations**

Solving Simultaneous Equations

This tip describes how to use formulas to solve simultaneous linear equations. The following

example shows a set of simultaneous linear equations:

3x + 4y = 8

4x + 8y = 1

Solving a set of simultaneous equations involves finding the values for
x and
y that satisfy both

equations. This set of equations has one solution:

x = 7.5

y = -3.625

The number of variables in the set of equations must be equal to the number of equations. The

preceding example uses two equations with two variables. Three equations are required in order

to solve for three variables (
and
z).

The general steps for solving a set of simultaneous equations follow. See Figure 128-1, which uses

the equations presented in the first paragraph of this tip.

Figure 128-1:
Using formulas to solve a set of two simultaneous equations.

1.
Express the equations in standard form.

If necessary, use basic algebra to rewrite the equations so that all variables appear on the

left side of the equal sign. The following two equations are identical, but the second one

is in standard form:

3x -8 = -4y

3x + 4y = 8