Independent and Dependent Variables and Linear Equations

two or more linear equations with the same variables

• piecewise defined function

• linear inequality

• solution to a linear inequality

• boundary line

• system of linear equations

Systems that produce coincident lines when graphed

• Independent System

• Dependent System

• Inconsistent Systems

• Consistent Systems

• Solution Region

y = mx + b

m = slope

b = y-intercept

• Slope Intercept Form

• Point-Slope Form

• Standard Form

• Equation for Slope

A system of linear equations can be consistent and independent. This is a system of linear equations having exactly one solution. The slopes of the lines defined by the equations are not equal, their y-intercepts could be equal or unequal.

• System of linear equation in two variables

• Consistent and Independent

• Consistent and Dependent

• Inconsistent

What is the graph of system of linear equation in two variables if it consistent and independent?

• coinciding lines

• intersecting lines

• parallel lines

• perpendicular lines

What is the graph of system of linear equation in two variables if it consistent and dependent?

• coinciding lines

• intersecting lines

• parallel lines

• perpendicular lines

What is the slope of the equation -10x + 5y = 15?

• 15

• 10

• 5

• 2

What is the y - intercept (b) of the equation -10x + 5y = 15?

• 15

• 10

• 3

• 2

What is the slope - intercept form of the equation -10x + 5y = 15?

• 5y = 10x + 15

• -5y = 10x + 15

• y = 2x - 3

• y = 2x + 3

Solve the system by substitution.
x + 12y = 68
x = 8y - 12

• Infinite Solutions

• (20, 4)

• (4, 20)

• No solution