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

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

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Answer 1 · 2016-01-28T04:27:53

$y = \frac{22}{37}$ $y = 22/37$ and $x =$ $x =$ -108/37#

Explanation:

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

$- 5 x - y = 14$ $-5x -y = 14$

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

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

Now we can plug that into the second equation:

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

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

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

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

Divide by $- 37$ $-37$ :
$x = \frac{108}{- 37}$ $x = 108/-37$

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

Add $y$ $y$ and subtract $14$ $14$ :
$\frac{540}{37} - 14 = y$ $540/37 - 14 = y$

Get a common denominator for $14$ $14$ :
$\frac{540}{37} - \frac{518}{37} = y$ $540/37 - 518/37 = y$

Subtract:
$\frac{22}{37} = y$ $22/37 = y$

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

1 Answer

Explanation:

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