Determine if the following systems of equations have one, none or infinitely many solutions.

x+3y=5
4x+12y=20

A. Infinite number of solutions

B. No Solution

C. One solution

D. No answer text provided.

A. Infinite number of solutions

Step-by-step explanation:

The given system of equations is expressed as

x + 3y = 5- - - - - - - - - - - - - -1

4x + 12y = 20- - - - - - - - - - - 2

We would apply the method of substitution. From equation 1, we would make x the subject by subtracting 3y from the left hand side and the right hand side of the equation. It becomes

x + 3y - 3y = 5 - 3y

x = 5 - 3y

Substituting x = 5 - 3y into equation 2, it becomes

4(5 - 3y) + 12y = 20

20 - 12y + 12y = 20

20 = 20

Therefore, the system of equations has an infinite number of solutions because as many values of x and y that satisfy the first equation, they would also satisfy the second equation.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

the answer is thin because within context, the stanza concludes the and frail tone the people have toward each other, and the fact that it would be thin, makes the most sense compared to "pliable" or "not hard or firm to the touch". hope this , good luck.

step-by-step explanation:

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