# How do you solve the following system: 2x+y=5, 5x+2y=12 ?

Mar 26, 2016

$x = 2$
$y = 1$

#### Explanation:

Given -

$2 x + y = 5$ ---------------(1)
$5 x + 2 y = 12$-------------(2)

Solve equation (1) for $y$

$y = 5 - 2 x$

Substitute $y = 5 - 2 x$ in equation (2)

$5 x + 2 \left(5 - 2 x\right) = 12$

Simplify and find the value of $x$

$5 x + 10 - 4 x = 12$
$x = 12 - 10$
$x = 2$

Substitute $x = 2$ in equation (1) and find the value of $y$

$2 \left(2\right) + y = 5$
$4 + y = 5$
$y = 5 - 4$
$y = 1$
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