EDGE Math 8

Example 2

Solve the following system of linear equations using the graphical method:

{\begin{array}{l} - 2 x + y = 1 \\ - 2 x + y = 3 \end{array}

Solution

The equations of the system can be written respectively as follows:

{\begin{array}{l} y = 2 x + 1 \\ y = 2 x + 3 \end{array}

The two lines have the same slope, which is equal to 2; however, they have different y-intercepts, which are 1 and 3, respectively. Hence, the two lines are distinct parallel lines, as shown in the graph below.

The solution set is the empty set, written as ${} .$ The system is inconsistent.

Graphical Method