Solve this system by elimination: 3x + 2y = 18 5x – 2y = 14

(4,3)

Step-by-step explanation:

3x + 2y = 18

5x – 2y = 14

Add the two equations together to eliminate y

3x + 2y = 18

5x – 2y = 14

8x    =   32

Divide each side by 8

8x/8 = 32/8

x = 4

Now determine the value for y

3(4) +2y = 18

12 +2y =18

Subtract 12 from each side

12-12+2y = 18-12

2y = 6

Divide by 2

2y/2 =6/2

y=3

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.

answer:   y=2x-3

step-by-step explanation: