Question

PLEASE HELP!!!!!!!!The system of equations is inconsistent.

Answer 1

$5x+ay=2 \\ bx+3y=8$

Write it in the y=mx+b form.

$ay=-5x+2 \\ 3y=-bx+8 \\ \\ y=-\frac{5}{a}x+\frac{2}{a} \\ y=-\frac{b}{3}x+\frac{8}{3}$

The system will be inconsistent when the equations describe two parallel lines.
Two lines are parallel when their slopes are identical.
$-\frac{5}{a}=-\frac{b}{3} \\ ab=(-5) \times (-3) \\ ab=15$

Also they can't be the same line, so the y-intercepts must be different.
$\frac{2}{a} \not= \frac{8}{3} \\ 8a \not= 2 \times 3 \\ 8a \not= 6 \\ a \not= \frac{6}{8} \\ a \not= \frac{3}{4}$

So for every value of a and b such that ab=15 and a≠3/2 this system of equations is inconsisent.

It can be:
$5x+5y=2 \\ 3x+3y=8$
or
$5x+15y=2 \\ x+3y=8$
or
$5x+\frac{1}{2}y=2 \\ 30x+3y=8$
etc.