Graphing systems

Question

graph the system below and write its solution: 

 

y=1/3x + 2

-2x + y= -3

Answer 1

The "system" is equations of two lines.  One is given in slope-intercept form and the other is given in (almost) Standard Form (actually, 2x-y=3).

 

Two points determine a line.  You can graph (that is, draw) a line using two points.  Just connect them and keep on going in each direction.

 

The line y=1/3x + 2  has points:

     (0,2)

     (3,3)

   [note: find easy ones]

 

The line -2x + y= -3  has points:

     (0,-3)

     (3,3)

 

Now, the "solution" is the point that is on both lines.  When you graph the lines, you will determine the coordinates of this point.  You may check your answer by plugging the (x,y) values of the point into both equations and verify that BOTH equations are satisfied.