X=4/3y-1 4y=3x+3

Question

Solve system of equations by graphing

Answer 1

To graph a line, all you need is two points.  That's because two points determine a line (remember that).  Drawing the line is like "connecting the dots" using a ruler.

 

If you have the opportunity to choose the two points, pick easy ones (unless you really like hard work).  Often, setting either x or y equal to 0 makes finding the other value easy.  Note:  when x=0 the line crosses the y-axis at the y-intercept; when y=0 the line crosses the x-axis at the x-intercept.  Let's use those points.

 

For  x=(4/3)y - 1,

     when x=0, y=3/4       point (0,3/4)

     when y=0, x=-1         point (-1,0)

 

For  4y=3x+3

     when x=0, y=3/4       point (0,3/4)

     when y=0, x=-1         point (-1,0)

 

The same two points --   (0,3/4) and (-1,0)  --  means that the two equations are for the same line.  Therefore, the "solution" is that all points that satisfy one equation also satisfy the other equation (since they are the same line).

Answer 2

Hi Zolan, if I read the equations correctly, they are the same line.

 

x = 4/3 * y - 1 is the same as 4y = 3x + 3, just rewritten differently.

 

The solution to the system is: 0 = 0, which means an infinite number of solutions.

 

Questions?