EDGE Math 8

Types of Systems of Two Linear Equations in Two Variables

Example 3

Classify the system of linear equations in two variables as consistent and independent, consistent and dependent, or inconsistent. Then graph the system.

{\begin{array}{l} 2 x + y = 5 \\ 4 x + 2 y = 10 \end{array}

Solution

Each equation can be written as $y = - 2 x + 5.$ Thus, both equations represent the same line. Therefore, the given system is consistent and dependent. Refer to the graph below.