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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

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