148. As many simultaneous quadratics differ somewhat from the type forms enumerated, the student must exercise his ingenuity in devising the necessary modifications of the foregoing methods.

When one of a set of homogeneous equations is truly homogeneous, it may sometimes be factored, yielding two simple equations.

When equations are symmetrical except as to algebraic signs, the method of symmetrical equations may be employed, that is, find the values of x + y and xy.

When equations are symmetrical or symmetrical except for algebraic signs, the following method is sometimes preferable.

1. The sum of two numbers is 7 and their product 12. Find the numbers.

Let x = one number and y

=

the other number.