Read each problem carefully and solve as required then answer the questions that follow.

Step-by-step explanation:

1) Number of jeans = x

Number of blouses = y

Total items = 6

x +  y = 6 (I)

       y = 6 - x

Cost of 'x' jeans =  300 *x = 300x

Cost of y blouses = 100 * y = 100y

Total amount  = Php. 1000

300x + 100y = 1000 (II)

2) Substitute y = 6 - x in equation (II)

         300x + 100(6-x) = 1000

300x + 6*100 - x *100 = 1000

 300x + 600 - 100x   = 1000

                200x + 600=1000

                          200x = 1000 - 600

                          200x = 400

                               x = 400/200

x = 2

Plugin x = 2 in equation (I)

2 + y = 6

     y = 6 - 2

     y = 4

Number of jeans = 2

Number of blouses = 4

3) This equations have only one solution. So, they are consistent and independent

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.