At one store, 5 pairs of jeans and 2 sweatshirts costs $207, while 3 pairs of jeans and 4 sweatshirts costs $169. find the cost of one sweatshirts

One pair of jeans cost $35.

One sweatshirt cost $16.

Step-by-step explanation:

j = jeans

s = sweatshirts

5j + 2s = $207

3j + 4s = $169

System of equations. You now must choose to either cancel out "j" or "s".

I'm going to cancel out the "s".

In order to cancel out the "s" you must make the number in front of each s the same number, but opposite. Meaning one is negative, and the other is positive.

2s and 4s. You can get 2 to 4 by multiplying by 2. And you want it to be negative. So you'll be multiplying the ENTIRE top equation by -2.

-2(5j+2s=207)

-2 x 5j = -10j

-2 x 2s = -4s

-2 x 207 = -414.

Rewrite the equation.

-10j - 4s = -414.

3j + 4s = 169.

You can now cancel out the "s"'s by adding them together. -4 + 4 = 0.

Now, you must add the other numbers, both "j"s and both of the totals.

-10j + 3j = -7j.

-414 + 169 = -245.

Put those numbers back into the equation..

-7j = - 245.

Divide both sides by -7 to get j by itself.

j = 35; each pair of jeans is worth $35.

Now, solve for "s" by plugging the value of j (35) into either of the ORGINAL equations. (5j + 2s = $207  OR 3j + 4s = $169)

5j + 2s = 207.

5(35) + 2s = 207.

175 + 2s = 207

Subtract 175 from both sides.

2s = 32

Divide both sides by 2.

s = 16; each sweatshirt costs $16.

$16.02

Step-by-step explanation:

x=Jeans y=Sweatshirts

5x+2y=207

3x+4y=169

3x=169-4y

3x/3=(169-4y)/3

x=56.33-1.33y

5(56.33-1.33y)+2y=207

281.66-6.66y+2y=207

281.66-207=4.66y

74.66=4.66y

74.66/4.66=y

y=16.02

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.