Question #21725

Question

1665 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-10T13:27:07

These two systems are inconsistent.

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

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

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

(subtract 6x)

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

(divide by -3)

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

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

(subtract 2x)

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

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