Question

How do I know whether a system of linear equations has either 1 solution, many solutions, or no solutions?? without solving the system.

Answer 1

look at the structure of the equations

Answer 2

if the are multiples of each other they are the same line and all points are in common

Answer 3

if they differ by a constant, they have no solutions since they are parallel lines that ride of into the sunset

Answer 4

any other situation only has one solutions

Answer 5

if you know about matrix determinants, then that would tell you, if the determinant is none zero, it has one solution, otherwise it has either no solution or many solutions

Answer 6

im assuming its the run of the barrel, ax+by=c linears of course

Answer 7

matrix sounds a bit to solvingish to me :)

Answer 8

@amistre64, good point...

Answer 9

well I'm in college remedial math. i'm very confused.. I learned y=mx+b .. for example.. i have these two equations, x=y-2, and y-x=3 ....How can I determine the solution by just looking at these two equations?

Answer 10

I mean, how can i determine how many solutions it has.. or if it even has one

Answer 11

youre asking how to do the math in your head without knowing how to do the math ....

Answer 12

we know the constants are different, so it either has 1 or none

Answer 13

if you can mentally put x and y to the same side; then the slope is the ratio of their coefficients such that -Xc/Yc = slope

Answer 14

or did i trip on my own genuis lol

Answer 15

x-y = -1/-1 = 1

-x+y = 1/1 = 1 .... parallels :)

no solution