7. Systems of Equations and Inequalities

Systems of Nonlinear Equations in Two Variables Practice Problems

7. Systems of Equations and Inequalities

Systems of Nonlinear Equations in Two Variables Practice Problems

66 problems

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1PRACTICE PROBLEM

Solve the given system of equations.

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2PRACTICE PROBLEM

Solve the system of logarithmic equations given below.

3PRACTICE PROBLEM

Solve the system of logarithmic equations given below.

4PRACTICE PROBLEM

Determine the dimensions of a rectangular wall if its perimeter and area are 40 feet and 64 square feet respectively.

5PRACTICE PROBLEM

Determine the dimensions of a rectangular wall if its perimeter and area are 40 feet and 64 square feet respectively.

6PRACTICE PROBLEM

Let x stand in for one number, and y for the other. Create a system of equations based on the information given below. Find the numbers by solving the system.

The squares of two numbers have a difference of five. Increasing three times the square of the first number by the square of the other number yields 31.

7PRACTICE PROBLEM

Let x stand in for one number, and y for the other. Create a system of equations based on the information given below. Find the numbers by solving the system.

The result of addition of first number and the other number is 14. The product of two numbers is 48.

8PRACTICE PROBLEM

Solve the given system of equations.

9PRACTICE PROBLEM

Solve the given system of equations.

10PRACTICE PROBLEM

Solve the given system of equations.

11PRACTICE PROBLEM

Solve the given system of equations.

12PRACTICE PROBLEM

Solve the given system of equations.

13PRACTICE PROBLEM

Solve the given system of equations.

14PRACTICE PROBLEM

Solve the given system of equations.

15PRACTICE PROBLEM

Solve the system of equations given below using the addition method.

16PRACTICE PROBLEM

Solve the system of equations given below using the addition method.

17PRACTICE PROBLEM

Solve the system of equations given below using the addition method.

18PRACTICE PROBLEM

Solve the system of equations given below using the addition method.

19PRACTICE PROBLEM

Work out the following system of nonlinear equations.

20PRACTICE PROBLEM

Work out the following system of nonlinear equations.

21PRACTICE PROBLEM

Solve the system of equations given below using the addition method.

22PRACTICE PROBLEM

Solve the system of equations given below using the substitution method.

23PRACTICE PROBLEM

Solve the system of equations given below using the substitution method.

24PRACTICE PROBLEM

Solve the system given below using the substitution method.

25PRACTICE PROBLEM

Solve the system given below using the substitution method.

26PRACTICE PROBLEM

Solve the system given below using the substitution method.

27PRACTICE PROBLEM

Solve the system given below using the substitution method.

28PRACTICE PROBLEM

Solve the system given below using the substitution method.

29PRACTICE PROBLEM

Solve the system given below using the substitution method.

30PRACTICE PROBLEM

Solve the system given below using the substitution method.

31PRACTICE PROBLEM

Consider the given rectangle. It has an area of 221 square meters and a perimeter of 60 meters. Find its length and width.

32PRACTICE PROBLEM

Solve the following system of equations using a method of your choice.

x² + y² = 9
x - y = 3

33PRACTICE PROBLEM

Solve the following system of equations using a method of your choice.

y = x² + 1
x + y = 1

34PRACTICE PROBLEM

Solve the following system of equations using a method of your choice.

y = x² + 4x + 4
x + y = 0

35PRACTICE PROBLEM

Out of two solutions of the given nonlinear system, one solution is (0, _):

36PRACTICE PROBLEM

Out of two solutions of the given nonlinear system, one solution is (_, 2):

37PRACTICE PROBLEM

What is the resulting equation when we substitute the solution for y in equation (2) into equation (1) to solve the given nonlinear system using the substitution method?

x² + 2y = 63 (1)

x - y = 0 (2)

38PRACTICE PROBLEM

Find two numbers using a system of nonlinear equations in two variables if they sum up to 64 and yield a product of 295 when multiplied.

39PRACTICE PROBLEM

Using a system of nonlinear equations in two variables, determine the two numbers whose sum of squares is equal to 130 and whose difference of squares is equal to 32.

40PRACTICE PROBLEM

For the indicated intersection points on the graph, check if they are solutions to the nonlinear system of equations given using the substitution method.

7x² = 9y + 9

3y = 7x - 3

41PRACTICE PROBLEM

For the indicated intersection points on the graph, check if they are solutions to the nonlinear system of equations given using the substitution method.

9y = 2x²

x²+ y²= 13