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3 years ago

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Solve this system of linear equations. separate the x- and y- values with a coma. -2x=8-6y

1 answer:

Alenkasestr [34]3 years ago

5 0

<span>The y variable has the same coefficient so use elimination (subtract equations).

-2x = 8 - 6y
-(-15x = 21 - 6y)
------------------------
13x = -13 + 0

x = -1
Use this to find y in either equation. </span>
<span>-2(-1) = 8 - 6y
2 = 8 - 6y
2 - 8 = -6y
-6 = -6y
y = 1

(x,y) = (-1, 1)
</span>

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$=\frac{d}{dx}[y]\sin(y)+y\frac{d}{dx}[\sin(y)]$

We must implicitly differentiate for y. This gives us:

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For the sin(y), we need to use the chain rule:

$u(v(x))'=u'(v(x))\cdot v'(x)$

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Simplify:

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Right Side:

We have:

$\frac{d}{dx}[x\cos(x)]$

This will be significantly easier since it's just x like normal.

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$=\frac{d}{dx}[x]\cos(x)+x\frac{d}{dx}[\cos(x)]$

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$=\frac{dy}{dx}\sin(y)+y\cos(y)\cdot\frac{dy}{dx}}=\cos(x)-x\sin(x)$

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$\frac{dy}{dx}(\sin(y)+y\cos(y))=\cos(x)-x\sin(x)$

Finally, divide everything by the expression inside the parentheses to obtain our derivative:

$\frac{dy}{dx}=\frac{\cos(x)-x\sin(x)}{\sin(y)+y\cos(y)}$

And we're done!

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