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P = Purple Marbles

Y = Yellow Marbles

Total number of marbles is 44.

P + Y = 44

There are 4 less purple marbles than yellow.

P = Y - 4

Substitute P in the original equation:

Y  + Y- 4 = 44

ax = b Formula - Take the four over to the other side:

Y + Y - 4 + 4 = 44 + 4

Y + Y = 48

2Y = 48

x = b Formula - Solve to find Y:

2Y / 2 = 48 / 2

Y = 24

Now find P

P = Y - 4

P = 24 - 4

P = 20

Check the answer is right by substituting both values into the original equation:

P + Y = 44

24 + 20 = 44

20 is 4 less than 24

28

Step-by-step explanation:

 Let P = the number of purple marbles

and Y = the number of yellow marbles. Then

                                         (1)          P + Y = 44

                                         (2)                P = 2Y -4

Substitute (2) into (1)             2Y - 4  + Y = 44

Combine like terms              3Y - 4        = 44

Add 4 to each side               3Y             = 48

Divide each side by 3     (3)    Y             = 16

Substitute (3) into (2)                           P = 2 × 16 - 4

                                                             P =   32    - 4

                                                             P =   28

There are 28 purple marbles.

Check:

(1) 16 + 28 = 44     (2) 28 = 2 × 16 - 4

      44     = 44           28 =    32   - 4

                                            28 = 28