let

x = the cost of 1 pencil

y = the cost of one pen

Five pencils and four pens cost $6.15

5x + 4y = 6.15

Three similar pens and eight similar pencils cost $9.85

8x + 3y = 9.58

we need to find how much is

8x + 7y = ?

we will add the following two equations

5x + 4y = 6.15 multiply both sides by -3

8x + 3y = 9.58 multiply both sides by 4

- 15x + 32x = (-3)*6.15 + 4*9.58

7x = 19.87 multiply both sides by 8/7

8x = (8/7)*19.87

lets add the 2 equations:

5x + 4y = 6.15 multiply both sides by 8

8x + 3y = 9.58 multiply both sides by (-5)

32y - 15y = 8*6.15 - 5*9.58

17y = 1.3

y = (1/17)*1.3

7y = (7/17)*1.3

8x + 7y = (8/7)*19.87 + (7/17)*1.3

8x + 7y = $23.244