# How do you solve the following system?:  11y=5x- 6 , 2y=7x-3

$x = \frac{21}{67}$ and $y = - \frac{27}{67}$

#### Explanation:

from the given equations

$11 y = 5 x - 6$ and $2 y = 7 x - 3$ rearrange the terms so that they become as follows

$5 x - 11 y = 6$ the 1st equation
$7 x - 2 y = 3$ the 2nd equation

Elimination by subtraction. Multiply the 2nd equation by $11$
and multiply the 1st equation by $2$ so that they become

$10 x - 22 y = 12$ the 1st equation
$77 x - 22 y = 33$ the 2nd equation

perform subtraction

$67 x + 0 = 21$

and $67 x = 21$

$x = \frac{21}{67}$

from the original 2nd equation, use $x = \frac{21}{67}$

$2 y = 7 x - 3$
$2 y = 7 \left(\frac{21}{67}\right) - 3$

$2 y = \frac{147}{67} - \frac{201}{67}$

$y = \frac{1}{2} \left(\frac{147 - 201}{67}\right)$

$y = \frac{1}{2} \left(\frac{- 54}{67}\right)$

$y = - \frac{27}{67}$

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