How do you solve $2 x + 2 y = 14$ $2x+2y=14$ and $2 x - y = 5$ $2x-y=5$ using substitution?

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Answer 1 · 2016-04-08T09:18:15

$x = 4, y = 3$ $x = 4, y = 3$

First you want to find a definition for either $x$ $x$ or $y$ $y$ in terms of the other, using the second equation.

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

Now you can substitute this into the first equation.

$2 x + 2 y = 14$ $2x + 2y = 14$
$2 x + 2 (2 x - 5) = 14$ $2x + 2(2x - 5) = 14$
$6 x - 10 = 14$ $6x - 10 = 14$
$6 x = 24$ $6x = 24$
$x = 4$ $x = 4$

With this value, substitute into anything and it should give you $y$ $y$ . Lets use the direct equation for $y$ $y$ we found.

$y = 2 x - 5$ $y = 2x - 5$
$y = 2 \cdot 4 - 5$ $y = 2 * 4 - 5$
$y = 3$ $y = 3$

You can substitute these values into any of the equations and they should work, if they are correct.

How do you solve 2x+2y=142x+2y=14 and 2x−y=52x-y=5 using substitution?