Question

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


`ax + 18y = 13 {a}^(2) - a`

`5x + (a - 1)y = 15`
For which value of a The system will have infinitely many solutions?
Step by step guide

Answer 1

I think your best bet is to eliminate y. To do this, solve the 2nd equation for y and subst. the result into the first equation, replacing y:

5(3-x)
5x + (a-1)y = 15 => (a-1)y = 5(3-x) => y = ----------
(a-1)

Substituting this result for y in the 2nd equation:
15-5x
5x + (a-1) * ----------- = 15
a-1

This can be simplified to 5x + 15 - 5x =15.

This equation is always true, for any x, for almost any a. Note that a cannot equal 1, because that would produce division by zero.