Solve Systems of Equations by Graphing: example 5.7

Solve the system by graphing: ${\begin{matrix} y = \frac{1}{2} x - 3 \\ x - 2 y = 4 \end{matrix} .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve each system by graphing: ${\begin{matrix} y = - \frac{1}{4} x + 2 \\ x + 4 y = - 8 \end{matrix} .$

How did it go?


To graph the first equation, we will use its slope and y-intercept.


To graph the second equation, we will use the intercepts.

Graph the lines.
Determine the point of intersection.	The lines are parallel.
	Since no point is on both lines, there is no ordered pair that makes both equations true. There is no solution to this system.


To graph the first equation, we will use its slope and y-intercept.


To graph the second equation, we will use the intercepts.

Graph the lines.
Determine the point of intersection.	The lines are parallel.
	Since no point is on both lines, there is no ordered pair that makes both equations true. There is no solution to this system.