How do you solve the system $2 x + y = 5$ $2x + y = 5$ and $x - 2 y = - 5$ $x - 2y = -5$ ?

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Answer 1 · 2015-05-22T15:02:57

You can isolate one variable in one equation and then substitute its value in the other, as follows.

Let's, for example, isolate $y$ $y$ in the first one.

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

Now, substitute it in the second:

$x - 2 (5 - 2 x) = - 5$ $x-2(5-2x)=-5$
$x - 10 + 4 x = - 5$ $x-10+4x=-5$
$5 x = 5$ $5x=5$
$x = 1$ $x=1$

Substituting this value in the $y = 5 - 2 x$ $y=5-2x$ ,

$y = 5 - 2 (1)$ $y=5-2(1)$
$y = 3$ $y=3$

How do you solve the system 2x + y = 52x+y=52x + y = 5 and x - 2y = -5x−2y=−5x - 2y = -5?