# Question #21725

Dec 10, 2016

These two systems are inconsistent.

#### Explanation:

$6 x - 3 y = 6$
$y = 2 x + 5$

to make $y$ the subject of both formulae:
$6 x - 3 y = 6$

$- 3 y + 6 x = 6$

(subtract 6x)

$- 3 y = - 6 x + 6$

(divide by -3)

$y = 2 x - 2$

final equations:
$y = 2 x - 2$
$y = 2 x + 5$

(subtract 2x)

$y - 2 x = - 2$
$y - 2 x = 5$

however, -2 is not equal to 5, so these equations are inconsistent (they have no solutions).