Can someone please give me an example of an System of linear equations that has no solution and explain why?

Answer 1

6x+3y=6
12x+6y=3

This has no solution because no set of x and y will satisfy both equations. You can prove it two ways:

1) Put them in slope-intercept form by solving for y:
y=-2x+2
y=-2x+1/4

The slopes (coefficient to x) are equal, and the constant is not. If the slopes were equal and the constants were the same, it would have infinity solutions.

2) Solve using substitution or elimination. If all your variables go away, and you are left with two constants then: a) if they are equal, the system has infinity solutions; b) if they are unequal the system has no solution

From our example, using elimination:

6x+3y=6
12x+6y=3

12x+6y=12
12x+6y=6
0=6

Using substitution:

6x+3y=6
12x+6y=3

y=-2x+2

12x+6(-2x+2)=3
12x-12x+12=3
12=3

There you go.

Answer 2

any system of equations must have the same number of equations as it has unknowns.

so any system of linear equations that has more unknowns than equtions has no solution, and is considered underdetermined.

That is as good as an explanation as you will find, my neighbor to the top.

Answer 3

x + y = +1
x + y = -1

Answer 4

Instead of bla, bla, bla, go to:

http://en.wikipedia.org/wiki/System_of_linear_equations

You have a great explanation...