Last month, he sold 50 chickens and 30 ducks for $550. this month, he sold 44 chickens and 36 ducks for $532
how much does a chicken cost, and how much does a duck cost?

The answer is chicken $8, duck $5

x - the cost of a chicken
y - the cost of a duck

he sold 50 chickens and 30 ducks for $550: 50x + 30y = 550
he sold 44 chickens and 36 ducks for $532: 44x + 36y = 532

50x + 30y = 550                divide by 10
44x + 36y = 550                 divide by 4

50x/10 + 30y/10 = 550/10
44x/4 + 36y/4 = 532/4

5x + 3y = 55                                    Multiply by (-3)
11x + 9y = 133

5x * (-3) + 3y * (-3) = 55 * (-3)
11x + 9y = 133

-15x - 9y = -165
11x + 9y = 133

Sum up:
-4x + 0y = -32
-4x = -32
x = -32/-4
x = 8

Since 5x + 3y = 55  and x = 8, then:
5 * 8 + 3y = 55
40 + 3y = 55
3y = 55 - 40
3y = 15
y = 15/3
y = 5