The local bookstore is having a sale on used books. nate bought 3 hardcover books and 7 paperback books and spent $29.50. tia bought 2 hardcover books and 5 paperback books and spent $20.50. what is the cost of a hardcover book?

cost of handcover book = $4

Step-by-step explanation:

LEt x be the cost of hardcover books and y be the cost of paperback books.

Nate bought 3 hardcover books and 7 paperback books and spent $29.50.

3x +7y= 29.50  equation 1

Tia bought 2 hardcover books and 5 paperback books and spent $20.50.

2x+5y= 20.50 equation 2

multiply the first equation by 2 and second equation by -3

6x   +14y = 59

-6x - 15y = -61.5

       -1y = -2.5

Divide both sides by -1

y= 2.5

2x+5y= 20.50

2x + 5(2.5)= 20.50

2x + 12.5 = 20.50

Subtract 12.5 on both sides

2x= 8

x= 4

So cost of handcover book = $4

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .