Question

ok thanksWhich is true about a system of equations that has no solutions?

A. The equations have the same slope.
B. The equations have the same x-intercept.
C. The equations have the same y-intercept.
D. The equations are the same.

Answer 1

creepy

Answer 2

A. Same slope

Answer 3

the equations have the same slope, so they are parallel and will never touch.

Answer 4

If two lines happen to have the same slope, but are not identically the same line, then they will never intersect. There is no pair (x, y) that could satisfy both equations, because there is no point (x, y) that is simultaneously on both lines. Thus these equations are said to be inconsistent, and there is no solution. The fact that they both have the same slope may not be obvious from the equations, because they are not written in one of the standard forms for straight lines. The slope is not readily evident in the form we use for writing systems of equations. (If you think about it you will see that the slope is the negative of the coefficient of x divided by the coefficient of y).