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What are x and y if $- 3 x + y = 6$ $-3x+y=6$ and $6 x - 2 y = 25 ?$ $6x-2y=25?$ ?

1 Answer

Oct 24, 2015

It is impossible for both
$XXX - 3 x + y = 6$ $color(white)("XXX")-3x+y=6$
and
$XXX 6 x - 2 y = 25$ $color(white)("XXX")6x-2y=25$
for any pair of values $(x, y)$ $(x,y)$

Explanation:

Given
[1] $XXX - 3 x + y = 6$ $color(white)("XXX")-3x+y=6$
and
[2] $XXX 6 x - 2 y = 25$ $color(white)("XXX")6x-2y=25$

If we multiply [1] by $(- 2)$ $(-2)$ , we get
[3] $XXX 6 x - 2 y = - 12$ $color(white)("XXX")6x-2y = -12$

Comparing [2] and [3], we have
$XXX 25 = - 12$ $color(white)("XXX")25 = -12$ (Impossible)

The given equations represent two parallel lines (they have no points in common).

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