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5 and 8

5. -3, -2/3

Step-by-step explanation:

5.

6x-4y=18

-x-6y=7        multiply this equation by 6 both sides

6x-4y=18

-6x-36y=42  add both equations

-4y-36y=18+42 combine like terms

-40y=60 so y = -4/6= -2/3

subtitute y=-2/3 in -x-6y=7

-x-6*(-2)/3=7 solve

-x+4=7 subtract 4 from both sides

-x=7-4

x= -3

8.

substitute y=4x+5 in to the second equation

12x-3(4x+5)=9

12x-12x-15=9

-15=9 is never true so the equation has no solutions

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.

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