−5x + y = −3
3x − 8y = 24

x = 0

y = -3

Step-by-step explanation:

-5x + y = -3 (I)

3x - 8y = 24 (II)

Multiply the equation (I) by 8

(I)*8    - 40x + 8y = -24

(II)         3x -  8y   =  24   {Add and y will be eliminated}

           -37x          = 0

                     x     = 0

Plugin x = 0  in equation(I)

-5*0 + y = -3

     0 + y = -3

           y = -3

- 5x + y =-3    1

3x -8y = 242

eqn 1 is multiply by 8 .we get -40 x +8y=-24 3

-40 x +8 y =-24 3

3 x   - 8y  = 24     2

·································

-37 x +0 = 0

··························

x =0

put x = 0 in equation 2

3 x -8 y =24

3×0 -8 y = 24

0 -8 y=24

-y =24÷8

-y =3

y = -3

ans ;

x = 0

y = -3

Step-by-step explanation:

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.