III. Elimination by Comparison.

115. Take again the equations,

5x+7y=43,

11x+9y=69.

Finding the value of x from the first equation, we have

and finding the value of x from the second, we obtain

Let these two values of x be placed equal to each other, and we have

This method of elimination is called the method by comparison, for which we have the following rule:

Find from each equation the value of the same unknown quantity to be eliminated.

Place these values equal to each other.

Exercises.

Find by the last rule the values of x and y from the following equations:

1. 3x+2+6=42, and y-2=143.

4

=

+

1

x+5, and ≈+= y − 34. Ans. x=2, y=9.

x y
2

y-2, and +=

= x — 13.

9. 4y=x+18, and 27 - y = x + y +4.

2

116. Having explained the principal methods of elimination, we shall add a few examples which may be solved by any one of them; and often, indeed, it may be advantageous to employ them all, even in the same example.

General Exercises.

Find the values of x and y in the following simultaneous

1. What fraction is that to the numerator of which if 1 be added the value will be, but if 1 be added to its denominator the value will be

2. A market-woman bought a certain number of eggs at 2 for a penny, and as many others at 3 for a penny; and, having sold them altogether at the rate of 5 for 2 pence, she found that she had lost 4 pence. How many of both kinds did she buy?