How do you solve the following system?: $9 x - 5 y = 21, - x - y = - 2$ $9x -5y =21, -x -y = -2$

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Answer 1 · 2018-06-27T02:21:50

$(\frac{31}{14}, - \frac{3}{14})$ $(31/14,-3/14)$

Let's start with the second equation by dividing every term by $- 1$ $-1$ . We now have the following system:

$9 x - 5 y = 21$ $color(blue)(9x-5y=21)$

$x + y = 2$ $x+y=2$

Let's subtract $x$ $x$ from both sides of the second equation. We get

$y = - x + 2$ $color(red)(y=-x+2)$

We can now plug this value into the blue equation. We get

$9 x - 5 (- x + 2) = 21$ $9x-5color(blue)((-x+2))=21$

Simplifying gives us

$9 x + 5 x - 10 = 21$ $9x+5x-10=21$

$\Rightarrow 14 x = 31$ $=>14x=31$

$\Rightarrow x = \frac{31}{14}$ $=>x=31/14$

We can plug this into the red equation to get

$y = - \frac{31}{14} + \frac{28}{14}$ $y=-color(red)(31/14)+28/14$

$y = - \frac{3}{14}$ $y=-3/14$

Therefore, our solutions are

$(\frac{31}{14}, - \frac{3}{14})$ $(31/14,-3/14)$

Hope this helps!

How do you solve the following system?: 9x−5y=21,−x−y=−29x -5y =21, -x -y = -2