EDGE Math 8

Types of Systems of Two Linear Equations in Two Variables

Example 1

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 \\ 2 x + y = 9 \end{array}

Solution

Write the equations of the system in the form $y = m x + b$ to compare the slopes m and the y-intercepts b of the lines.

{\begin{array}{l} y = - 2 x + 5 \\ y = - 2 x + 9 \end{array}

The two lines have the same slope, which is –2. They have different y-intercepts, which are 5 and 9. The system has no solution; hence, it is inconsistent. Refer to its graph below.