David bought three DVDs in for books for $40 at a yard sale and I bought one DVD and six books for $18 how much did each DVD and book cost

Answer: One DVD is $12 and one book is $1

Step-by-step explanation:

Let the DVD be d and the book be b.

Case 1:

3d + 4b = $40 ... (1)

Case 2:

1d + 6b = $18 ... (2)

In this equations above, I intend to eliminate variable d, so I'm going to multiply the coefficient of d in (1) to multiply (2)

3 * (1d + 6b = 18)

3d + 18b = 54 ... (3)

Then, subtract (1) from (3)

3d + 18b = 54

- (3d + 4b = 40)

3d - 3d + 18b - 4b = 54 - 40

0 + 14b = 14

b = 14/14

b = 1.

Then substitute 1 for b in (2)

1d + 6 (1) = 18

d + 6 = 18

d = 18 - 6

d = 12.

(d, b) = (12,1)