Solve the equations -9x + 2y = 23 and -4x - y = -3

(-1,7)

Step-by-step explanation:

-9x + 2y = 23

-4x - y = -3

multiplying equation 2 by 2

-9x + 2y = 23

-8x - 2y = -6

adding the two equation to cancel out y

-17x = 17

x = -1

plugging back x = -1 into the second equation

4 - y = -3

-y = -7

y = 7

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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