How do you solve the following system: $7y - 2x = 10, -5x − y = 14$ ?

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Answer 1 · 2016-01-28T04:27:53

$y = 22/37$ and $x =$ -108/37#

Let's solve the second equation for y, which should be simply since it doesn't have a coefficient. It starts off as:

$-5x -y = 14$

Add y to both sides and subtract 14 from both sides:

$-5x - 14 = y$ , or in reverse: $y = -5x - 14$ .

Now we can plug that into the second equation:

$7(-5x - 14) - 2x = 10$

Multiply through: (tip: $7 * 14$ is $98$ )
$-35x - 98 - 2x = 10$

Consolidate $x$ 's:
$-37x - 98 = 10$

Add $98$ to both sides:
$-37x = 108$

Divide by $-37$ :
$x = 108/-37$

Now plug that back into the initial equation:
$-5 * 108/-37 - y = 14$
$540/37 - y = 14$

Add $y$ and subtract $14$ :
$540/37 - 14 = y$

Get a common denominator for $14$ :
$540/37 - 518/37 = y$

Subtract:
$22/37 = y$

How do you solve the following system: 7y - 2x = 10, -5x − y = 14 7y - 2x = 10, -5x − y = 14 ?