which system of linear equations has only one solution?

Question

A) x+2y=-1

    2x+5y=0

B)3x-y=9

   6x-2y=6

C)y=2x-3

   -4x+2y=-6

D) x-y=4

    y=x+4

Answer 1

In case this is just an algebra class (rather than linear algebra assumed in the previous answers)...

 

All you need to check is whether the x and y coefficients scale up/down the same amount.  If they do, the system either has 0 or infinitely many solutions, because both equations would have the same slope if written in slope-intercept form (y=mx+b).  (Remember that the solution of a system of linear equations is where they cross on a graph?)  So for example, look at 3x - y = 9 and 6x - 2y = 6. If you multiply the first equation by 2, the left side is 6x - 2y which is exactly like the other equation!  Now, you may need to move stuff around (like by adding y to both sides or whatever) to get the equations to look the same, because the signs need to match as well.  I hope this helps!

Answer 2

Just evaluate the principal determinant of each system.  If it is not zero, there is one solution.