Question

How many solutions exist for the system of equations given below?

3a + 4b = 20
12a = 80 − 16b

A. One Solution

B. Two Solutions

C. Infinitely many solutions

D. No solutions

Answer 1

3a + 4b = 20
4b = 20 - 3a
b = 5 - 3/4 a
12a = 80 - 16(5 - 3/4 a)
12a = 80 - 80 + 12a
12a = 12a
C. Infinitely many solutions

Answer 2

3a+4b = 20

rewrite the second equation by adding 16b to each side

12a+16b = 80

divide each side by 4

3a+4b = 20

they are the same equation,

there are infinitely many solutions