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316 Chapter 7 Equations and Inequalities
Lesson
7.4
EXAMPLE
Identifying Solutions of Equations in Two Variables
1
EXAMPLE
Using an Equation in Two Variables
2
Tell whether the ordered pair is a solution of the equation.
a. y 2x; (3, 6) b. y 4x 3; (4, 12)
6
?
2(3) Substitute. 12
?
4(4) 3
6 6
✓ Compare. 12 13
✗
So, (3, 6) is a solution. So, (4, 12) is not a solution.
You can use equations in two variables to represent situations involving
two related quantities. The variable representing the quantity that
can change freely is the independent variable. The other variable is
called the dependent variable because its value depends on the
independent variable.
The equation y 128 8x gives the amount y (in fl uid ounces) of milk
remaining in a gallon jug after you pour x cups.
a. Identify the independent and dependent variables.
Because the amount y remaining depends on the number x
of cups you pour, y is the dependent variable and x is the
independent variable.
b. How much milk remains in the jug after you pour 10 cups?
Use the equation to fi nd the value of y when x 10.
y 128 8x
Write the equation.
128 8(10) Substitute 10 for x.
48 Simplify.
There are 48 fl uid ounces remaining.
Tell whether the ordered pair is a solution of the equation.
1. y 7x; (2, 21) 2. y 5x 1; (3, 16)
3. The equation y 10x 25 gives the amount y (in dollars) in
your savings account after x weeks.
a. Identify the independent and dependent variables.
b. How much is in your savings account after 8 weeks?
Exercises 6–11
and 13–17
Lesson Tutorials
Key Vocabulary
equation in two
variables, p. 316
solution of an
equation in two
variables, p. 316
independent variable,
p. 316
dependent variable,
p. 316
An equation in two variables represents two quantities that change in
relationship to one another. A solution of an equation in two variables is
an ordered pair that makes the equation true.