graph 6x - 2y =2 9x-3y=1

Question

graph 6x - 2y =2 9x-3y=1 

if the system has an infinite number of solutions use set builder to write the solution set. if a system has no solution. state this

Answer 1

6x - 2y = 2             eq1

9x - 3y = 1             eq2

 

 

First, we need to get these equations in y=mx+b from, where m is slope and b is y-intercept.

 

Start with eq1

 

-2y = -6x + 2

 

  y = 3x - 1

 

 

Do the same to eq2

 

-3y = -9x + 1

 

   y = 3x - (1/3)

 

 

Now, that we have the equations in the form we want, we can easily graph them.

 

For eq1, start plotting the point (0, -1).  Then use the slope to find the other point.  Move 1 unit to the right, then movie 3 units upward.  The new point is (1, 2).   Now, connect these points to get the line of the equation.

 

For eq2, use the same procedure as done in eq1.  Start with the point (0, -1/3).  Then use the slope to find the next point.  Draw a line connecting those two points.

 

 

Once you have your two lines, look for the point of intersection.  This point of intersection is the solution to the system of equations.  Since the two lines have the same slope, they will never intersect. 

 

Therefore, there is no point of intersection.