EDGE Math 8

Types of Systems of Two Linear Equations in Two Variables

Example 2

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 \\ 3 x + y = 4 \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 = - 3 x + 4 \end{array}

The two lines have different slopes, namely, –2 and –3. Hence, the given system is consistent and independent. See the figure below.