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3 years ago

How do I solve system of equations by substitution 3x-7y=41 x=-2y-21

Mathematics

2 answers:

Butoxors [25]3 years ago

8 0

Answer:

(-5;-8)

Step-by-step explanation:

-6y-63-7y=41

-13y=104

y=-8

x=-2*-8-21=-5

Rashid [163]3 years ago

5 0

Going off the value of x in terms of y given in the second equation, we can substitute the x in the first equation with the value -2y - 21 to give us the equation

3(-2y - 21) - 7y = 41

Distributing the 3 to the -2y and -12:

-6y - 63 -7y = 41

Combining like terms:

-13y - 63 = 41

Adding 63 to either side:

-13y = 104

And dividing both sides by -13:

y = -8

We can plug in this solution for y to the second equation to obtain a solution for x:

x = -2(-8) - 21
x = 16 - 21
x = -5

So our solution is the pair (-5, -8).

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Answer:

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Step-by-step explanation:

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2 years ago

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pishuonlain [190]

Using a trigonometric identity, it is found that the values of the cosine and the tangent of the angle are given by:

$\cos{\theta} = \pm \frac{2\sqrt{2}}{3}$

$\tan{\theta} = \pm \frac{\sqrt{2}}{4}$

<h3>What is the trigonometric identity using in this problem?</h3>

The identity that relates the sine squared and the cosine squared of the angle, as follows:

$\sin^{2}{\theta} + \cos^{2}{\theta} = 1$

In this problem, we have that the sine is given by:

$\sin{\theta} = \frac{1}{3}$

Hence, applying the identity, the cosine is given as follows:

$\cos^2{\theta} = 1 - \sin^2{\theta}$

$\cos^2{\theta} = 1 - \left(\frac{1}{3}\right)^2$

$\cos^2{\theta} = 1 - \frac{1}{9}$

$\cos^2{\theta} = \frac{8}{9}$

$\cos{\theta} = \pm \sqrt{\frac{8}{9}}$

$\cos{\theta} = \pm \frac{2\sqrt{2}}{3}$

The tangent is given by the sine divided by the cosine, hence:

$\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}$

$\tan{\theta} = \frac{\frac{1}{3}}{\pm \frac{2\sqrt{2}}{3}}$

$\tan{\theta} = \pm \frac{1}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}$

$\tan{\theta} = \pm \frac{\sqrt{2}}{4}$

More can be learned about trigonometric identities at brainly.com/question/24496175

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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