Question

3x+4y=5

2x-5y=8
Is this consistent and independent, consistent and dependent, or inconsistent

Answer 1

3x + 4y = 5
2x - 5y = 8

To answer this question, we need to put both of these equations into Slope-Intercept form, or in other words, solve for y.

3x + 4y = 5 Subtract 3x from both sides
4y = -3x + 5 Divide both sides by 4
y =
`-(3)/(4)` +
`(5)/(4)`

2x - 5y = 8 Subtract 2x from both sides
-5y = -2x + 8 Divide both sides by -5
y =
`(2)/(5)` -
`(8)/(5)`

When you look at the two equations, you can see that their slopes are completely different, so they aren't parallel, or inconsistent. Since
`(2)/(5)` is not the same as
`-(3)/(4)`, they aren't the same line, or dependent. So, the only option left is that they are consistent and independent.