From the second,

2; hence y=4.

22. Find the values of x and y in the Equations
x2y-xy-6, and x3y-y=21.

Dividing the first Equation by the second,

Reducing each member of this Equation to its lowest terms,

from which x will be found 2, or ; and we shall now easily find y=3, or -24.

23. Find the values of x and y in the Equations

x3+xy239, and x2y+y3-26.

Substituting this value of y in the first Equation,

24. Find the values of x and y in the Equations

x-y=4, and x3-y33-16.

Dividing each side of the second Equation by the corresponding side of the first,

The value of x will now be found to be 7, or -3.

25. Find the values of x and y in the Equations

x2-y2-5, and xa—ya—65.

Dividing the second Equation by the first,

x2+y21-3.

Adding this Equation to the first,

2x218; then x=±3.

Substituting this value of x in the first Equation, we shall find y

=±2.

26. Find the values of x and y in the Equations

x+y=60, and 2(x2+y2)=5xy.

Substituting this value of x for x in the first Equation,

from which y will be found equal to 40, or 20; and x is now easily found equal to 20, or 40.

27. Find the values of x and У in the Equations

Substituting for xy in this Equation, its value from the first Equation,

Substituting this value of 23 in the fourth Equation,

28. Find the values of x and y in the Equations

xy=25, and 23+y3=10xy.

Substituting the values of xy and x3 in the second Equation,

Clearing this Equation of fractions,

15625+y=250y3;

from which y3 will be found = 125; hence y=5. Substituting 5 for y in the first Equation, we find x=-5.

29. Find the values of x and y in the Equations

x2'—y2—(x+y)=8, and (x−y)2(x+y)=32.

Equating this value of (x-y)2, with its value in the fourth Equation,

Developing, and clearing this Equation of fractions, by multiplying it by (x+y)2, we shall find

64+16(x+y)+(x+y)2=32(x+y).

Transposing, and uniting similar terms,

(x+y)2-16(x+y)=-64.

This Equation will give x+y=8; then x=8—y.
Substituting this value of x in the first Equation,

64-16y-88; hence y=3.

Then since x=8-y, we have x= —8—3—5.

30. Find the values of x and y in the Equations,

x+√xy+y=7, and x2+xy+y2=21.

Dividing the second Equation by the first,

x−√xy+y=3.

Substituting this value of x in the fifth Equation,

31. Find the values of x and y in the Equations

Equating the two values of√xy from the second and third Equations,

Clearing this Equation of fractions, and reducing,

20xy=5(x+y)2—64(x+y).

Dividing this Equation by 5, and subtracting the result from the fifth Equation,