Solve Systems of Equations by Graphing: example 5.8

Solve the system by graphing: ${\begin{matrix} y = 2 x - 3 \\ −6 x + 3 y = - 9 \end{matrix} .$

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: ${\begin{matrix} y = - 3 x - 6 \\ 6 x + 2 y = - 12 \end{matrix} .$

How did it go?


Find the slope and y-intercept of the first equation.
Find the intercepts of the second equation.

Graph the lines.
Determine the point of intersection.	The lines are the same!
	Since every point on the line makes both equations true, there are infinitely many ordered pairs that make both equations true.
	There are infinitely many solutions to this system.


Find the slope and y-intercept of the first equation.
Find the intercepts of the second equation.

Graph the lines.
Determine the point of intersection.	The lines are the same!
	Since every point on the line makes both equations true, there are infinitely many ordered pairs that make both equations true.
	There are infinitely many solutions to this system.