Equations in Two Variables

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Presentation transcript:

Equations in Two Variables Chapter 8 Section 8.1

Objective Students will solve equations in two variables over given domains of the variables

Vocabulary One-variable equations Two-variable equations Solution Ordered pair Solved

Concept In earlier chapters, you worked with equations that contained only one variable. In this chapter, you will work with equations that contain two different variables.

Concept One variable equations 2x – 3 = 7 1 – y = 9 x2 + 5x + 4 = 0 Two variable equations 4x + 3y = 10 xy = 6 x2 + y2 = 4

Concept The solution to equations in one variable are numbers. The solutions to equations in two variables are pairs of numbers. For example, the pair of numbers x = 1 and y = 2 is a solution of the equation 4x + 3y = 10 because 4(1) + 3(2) = 10

Concept The solution x = 1 and y = 2 can be written as (1, 2), with the x-value written first. A par of numbers, such as (1, 2), for which the order of the numbers is important, is called an ordered pair.

Concept To determine whether an ordered pair is a solution to an equation you must substitute the values in for the correct variable and solve. If the equation equals what it is supposed to then the ordered pair is a solution.

Example State whether each ordered pair of numbers is a solution of 4x + 3y = 10 a. (4, -2) b. (-2, 6) c. (3/2, 4/3) d. (3, -1)

Concept The equation 4x + 3y = 10 has many solutions. However, if both x and y are required to be whole numbers, then (1, 2) is the only solution. When you find the set of all solutions of an equation, whether it is a one-or two-variable equation, you have solved the equation.

Concept To determine what ordered pairs are solutions in a specific domain, you must first solve the equation for y. Once the equation set equal to y, you then replace x with successive whole numbers and find the corresponding values of y. If y fits in the domain you have found a solution pair.

Solve (x + 1)y = 3 if x & y are whole numbers Example Solve (x + 1)y = 3 if x & y are whole numbers

Solve 5x + y = 7 if x & y are whole numbers Example Solve 5x + y = 7 if x & y are whole numbers

Concept When solving equations in two-variables, we will give the numbers in a solution pair in the alphabetical order of the variables.

Questions

Assignment Worksheet