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Helen [10]
3 years ago
14

Which statement is true about the equations –3x + 4y = 12 and 1/4x –1/3 y = 1?The system of the equations has exactly one soluti

on at (–8, 3). The system of the equations has exactly one solution at (–4, 3). The system of the equations has no solution; the two lines are parallel. The system of the equations has an infinite number of solutions represented by either equation.
Mathematics
1 answer:
iren [92.7K]3 years ago
4 0

Answer:

The system of the equations has no solution; the two lines are parallel.

Step-by-step explanation:

The equations have the same slope. In standard form, this can be seen as the same coefficients for x and y. We will multiply the second equation by -12 to reveal this.

\frac{1}{4} x-\frac{1}{3}y=1 \\-12(\frac{1}{4} x-\frac{1}{3}y=1)\\\frac{-12}{4} x-\frac{-12}{3}y=-12\\-3x+4y=-12

This means the equations are parallel and will never cross. There is no solution.

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Option B:

Law of cosine, two sides and the included angle are known.

Solution:

Let us first know the law of cosines and law of sines.

Law of cosine:

If we know the sides a, b and the included angle θ, then we can find the third side c. This is known as the law of cosine.

c^2=a^2+b^2-2abcos\theta

Law of sine:

The sides of a triangle are to one another  in the same ratio as the sines of their opposite angles.

$\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}

Given ∠P and the sides r, q are known.

<u>To find the value of p:</u>

Option A: Law of cosines, all sides are known.

It is false by the above definition of law of cosine.

Option B: Law of cosine, two sides and the included angle are known.

It is true by the above definition of law of cosine.

Option C: Law of sines, all sides are known.

It is false, because one angle is given in question.

Option D: Law of sines, two angles and the included side are known.

It is false, because two angles are not given.

Option B is the correct answer.

Hence the answer is "Law of cosine, two sides and the included angle are known".

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