There are a number of ways of accomplishing this task.
This is one way that you should
consider using if you do not already have a technique the works reliably. I will
demonstrate this first for a set of two equations in two unknowns and then for
equations in three unknowns. If you have a larger set the technique works quite
the amount of time you will need to spend grows quickly.
Now I pick one of the two variables to eliminate. I look
for an easy relationship between
the coefficients. In this case the coefficients of the y variable qualify. The
idea is to multiply one ( or both ) equations by some number ( or pair of numbers ) so that
y coefficients ( because I picked on y ) are equal and opposite. Then when I add
equations ( I can add the same value to both sides of an equation and still have
equality. ) the resulting coefficient for y will be zero . I will schematically
operation in this way
This says that equation (3) will be the sum of equation (1) and 4 times equation
will write equation (1) on one line, 4 times equation (2) on the next line, and
then the sum
of the two on the third line.
I can solve (3) for x by multiplying both sides by
With this value for x in hand I may select either (1) or
(2) and replace x with . I will
And thus we have the values for x and y that satisfy both
of our initial equations. Starting
on the next page I will use the same procedure for a system of three equations
unknowns. I will not put in all of the commentary or all of the steps . See if
supply those for yourself.
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