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4 years ago

Solve 3x+2y=7 and x-4y=-21 by using any method

Mathematics

1 answer:

kupik [55]4 years ago

8 0

Answer:

(- 1, 5 )

Step-by-step explanation:

Using the method of substitution.

Given the 2 equations

3x + 2y = 7 → (1)

x - 4y = - 21 → (2)

Rearrange (2) expressing x in terms of y by adding 4y to both sides.

x = 4y - 21 → (3)

Substitute x = 4y - 21 into (1)

3(4y - 21) + 2y = 7 ← distribute and simplify left side

12y - 63 + 2y = 7

14y - 63 = 7 ( add 63 to both sides )

14y = 70 ( divide both sides by 14 )

y = 5

Substitute y = 5 into (3)

x = (4 × 5) - 21 = 20 - 21 = - 1

Solution is (- 1, 5 )

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2 years ago

Calculating cos-1 ( help is gladly appreciated :) )

Alekssandra [29.7K]

Answer:

$\frac{3\pi}{4}$

(Assuming you want your answer in radians)

If you want the answer in degrees just multiply your answer in radians by $\frac{180^\circ}{\pi}$ giving you:

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We can do this since $\pi \text{ rad }=180^\circ$ (half the circumference of the unit circle is equivalent to 180 degree rotation).

Step-by-step explanation:

$\cos^{-1}(x)$ is going to output an angle measurement in $[0,\pi]$ .

So we are looking to solve the following equation in that interval:

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This happens in the second quadrant on the given interval.

The solution to the equation is $\frac{3\pi}{4}$ .

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