Question

Solve the following system of equations.
x - 2y = 6
2x - 4y = 10

Infinitely Many Solutions

No Solutions

(0, 0)

(6, 10)

Answer 1

multiply the first equation all the way across by 2
you get \(2x-4y=12\)
now there is no way for \(2x-4y\) to be \(12\) and at the same time for \(2x-4y\) to be \(10\)
therefore there is no solution

Answer 2

sometimes you'll have a case where one equation is a multiple of the other. that case gives you infinitely many solutions.

Answer 3

thank you

Answer 4

if you do the work all the way through in such a case, you'll end up with 0=0 or something similar. if the final number statement is true, you have infinitely many solutions. if the final number statement is false, such as in this problem, you have no solutions.

Answer 5

alright thanks :)