How do you solve the system of equations $13x - 5y = 20$ and $13x - 5y = 10$ ?

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Answer 1 · 2016-12-07T11:32:55

The system has no solution because its equations are incompatible.

Solve a system like this:

$13 x - 5 y = 20$
$13 x - 5 y = 10$

means we have to find values $x$ and $y$ that makes true both equations at same time.

In that system we have here, if we try to solve it, for example, using reduction method, we obtain something like that:

$color(white) "....." 13 x - 5 y = 20$
$- (13 x - 5 y = 10)$
$"—————————"$
$color(white) "................." 0 = 10$

i.e. a false identity. This means that no exists any value for $x$ and $y$ that match both equations at same time, i.e. system is incompatible.

How do you solve the system of equations 13x - 5y = 2013x - 5y = 20 and 13x - 5y = 1013x - 5y = 10?