Question

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

What are the missing values?

5x+____y=2
____x+3y=8

Answer 1

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

Write it in the y=mx+b form.


`ay=-5x+2 \\ 3y=-bx+8 \\ \\ y=-(5)/(a)x+(2)/(a) \\ y=-(b)/(3)x+(8)/(3)`

The system will be inconsistent when the equations describe two parallel lines.
Two lines are parallel when their slopes are identical.

`-(5)/(a)=-(b)/(3) \\ ab=(-5) * (-3) \\ ab=15`

Also they can't be the same line, so the y-intercepts must be different.

`(2)/(a) \\ot= (8)/(3) \\ 8a \\ot= 2 * 3 \\ 8a \\ot= 6 \\ a \\ot= (6)/(8) \\ a \\ot= (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+(1)/(2)y=2 \\ 30x+3y=8`
etc.