Answer:
a = 673; b = 2; c = 674
Step-by-step explanation:
ab + c = 2020
a + bc = 2021
Add the equations
ab + c + a + bc = 4041
Rearrange the left side.
ab + bc + a + c = 4041
Factor the left side.
b(a + c) + 1(a + c) = 4041
(a + c)(b + 1) = 4041
Find the prime factors of 4041.
4010 = 3² × 449
The factors of 4041 are 1, 3, 9, 449, 1347, 4041
Back to
(a + c)(b + 1) = 4041
Pick two factors of 4041 whose product is 4041.
Try 449 and 9.
Let a + c = 1347 and b + 1 = 3
b + 1 = 3
b = 2
Original equations with b = 2.
2a + c = 2020
a + 2c = 2021
Solve simultaneously for a and c.
2a + c = 2020
-2a - 4c = -4042
Add the equations above.
-3c = -2022
c = 674
2a + c = 2020
2a + 674 = 2020
2a = 1346
a = 673
Answer: a = 673; b = 2; c = 674
