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

May 20, 2018

no solutions

#### Explanation:

you solve by elimination:

$x + 2 y = 10$
$2 x + 4 y = 10$

$- 2 \left(x + 2 y = 10\right)$
$2 x + 4 y = 10$

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

$0 = - 10$

since this is not possible there are no solutions.

May 20, 2018

$\text{see explanation}$

#### Explanation:

$x + 2 y = 10 \to \left(1\right)$

$2 x + 4 y = 10 \to \left(2\right)$

$\text{equation "(2)" is a multiple of equation } \left(1\right)$

$\text{thus they are parallel lines with no point of intersection}$

$\text{hence there is no solution}$