How many solutions does this system have?

Question

 x-3y=4 -2x+6y=3

Answer 1

   x  - 3y = 4

-2x + 6y = 3

 

Multiply the first equation by 2:

 

2·(x - 3y = 4)

2x - 6y = 8

 

Now add it to the second equation:

 

-2x + 6y = 3

 2x -  6y = 8

---------------

  0  +  0 = 11

  0 = 11

 

No solutions

Answer 2

For an equation of a line in Standard Form (Ax+By=C), the slope is (-A/B).

The slope of x-3y=4 is (-1/-3).

The slope of -2x+6y=3 is (-2/6) = (-1/3).

The lines have the same slope.

 

The y-intercept [that is, the point(0.B] is (0,C/B).

The y-intercept of x-3y=4  is (0,-4/3).

The y-intercept of  -2x+6y=3  is (0,3/6) = (0,1/2)

These are not the same line.

 

The lines have the same slope, but different y-intercepts, so they never cross.  There is no solution.