System of linear equations

Question

Given this system of linear equations where {a} is parameter.

ax + 18y = 13a² - a

5x + (a - 1)y = 15

For which value of a The system will have infinitely many solutions? Step by step guide, please.

Answer 1

For the system to have an infinite number of solutions one equation must be a multiple of the other.

 

5 / a = (a - 1) / 18

90 = a² - a

0 = a² - q - 90

0 = (a - 10)(a + 9)

 

a is either 10 or -9.