Intermediate Algebra (11th edition)

SECTION 11.4 Nonlinear Systems of Equations 663

Solve each system by the elimination method or a combination of the elimination and substi-
tution methods. See Examples 3 and 4.

3 x^2 + 4 y^2 = 39

5 x^2 - 2 y^2 =- 13

x^2 + 2 y^2 = 4

3 x^2 + 2 y^2 = 12

31. 32.

3 x^2 + 4 y^2 = 36

6 x^2 + y^2 = 9

x^2 + 3 y^2 = 3

2 x^2 + 3 y^2 = 6

33. 34.

4 x^2 + 3 y^2 = 36

x^2 + 6 y^2 = 9

4 x^2 - 5 y^2 = 28

2 x^2 + y^2 = 28

35. 36.

2 y^2 = 2 - x^2

5 x^2 = 20 - 5 y^2

3 x^2 = 24 - 4 y^2

2 x^2 = 8 - 2 y^2

37. 38.

x^2 +y^2 = 6

2 x^2 + 3 xy+ 2 y^2 = 21

x^2 +y^2 = 10

x^2 +xy+y^2 = 15

39. 40.

2 x^2 - 3 xy+ 3 y^2 = 4

• 2 x^2 + 7 xy- 3 y^2 = 4


• x^2 - 3 xy+ y^2 = 3

3 x^2 + 2 xy- 3 y^2 = 5

Use a graphing calculator to solve each system. Then confirm your answer algebraically.

Solve each problem by using a nonlinear system.

43.The area of a rectangular rug is 84 and its perimeter is 38 ft. Find the length and width
of the rug.

44.Find the length and width of a rectangular room whose perimeter is 50 m and whose area
is 100.

45.A company has found that the price p(in dollars) of its
scientific calculator is related to the supply x(in thou-
sands) by the equation

The price is related to the demand x(in thousands) for the

calculator by the equation

The equilibrium priceis the value of pwhere demand

equals supply. Find the equilibrium price and the supply/

demand at that price. (Hint:Demand, price, and supply

must all be positive.)

46.The calculator company in Exercise 45has determined
that the cost yto make x(thousand) calculators is

while the revenue yfrom the sale of x(thousand) calculators is

Find the break-even point,where cost equals revenue.

Graph each inequality. See Section 3.4.

47. 2 x-y... 4 48.-x+ 3 y 79

PREVIEW EXERCISES

36 x^2 - 3 y=0.

y= 4 x^2 + 36 x+20,

p= 10 x+12.

px=16.

m^2

ft^2

x+y=- 1 y=-x^2 - 1

xy=- 6 y= 2 x^2 + 4 x