Question

How do you tell whether the system `x + 2y = 10` and `2x + 4y = 10`has no solution or infinitely many solutions?

Answer 1

no solutions

Explanation:

you solve by elimination:

`x + 2y = 10`
`2x + 4y = 10`

`-2(x + 2y = 10)`
`2x + 4y = 10`

`-2x -4y = -20)`
`2x + 4y = 10`

add them together:

`0 = -10`

since this is not possible there are no solutions.

Answer 2

`"see explanation"`

Explanation:

`x+2y=10to(1)`

`2x+4y=10to(2)`

`"equation "(2)" is a multiple of equation "(1)`

`"thus they are parallel lines with no point of intersection"`

`"hence there is no solution"`