How do you solve this system of equations: $2 x - 3 = y and y - 2 x = - 5$ $2x - 3= y and y - 2x = - 5$ ?

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Answer 1 · 2017-10-06T23:14:31

No solution

Change the second equation so that it is set equal to $y$ $y$ :

$y - 2 x = - 5 \to y = 2 x - 5$ $y-2x=-5->y=2x-5$

Then set the two equations equal to each other (equal values method):

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

$2 x - 3 = 2 x - 5$ $2x-3=2x-5$

Subtract 2x on both sides:

$- 3 = - 5$ $-3=-5$

This is a false statement, so there is no solution.

These two equations have no points in common, it can be shown visually as two parallel lines that never intersect:

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Answer 2 · 2017-10-07T01:59:32

There is no solution. They are parallel lines.

$2 x - y = 3$ $2x - y = 3$
$- 2 x + y = - 5$ $−2x + y = −5$ Add the two equations.
$0 = - 2$ $0 = -2$ NO SOLUTION

How do you solve this system of equations: 2x−3=yandy−2x=−52x - 3= y and y - 2x = - 5?