Question

Determine if the lines are Parallel,Perpendicular or neither .

6x+10y=20 and 5x-3y=21 show steps please

Answer 1

6x+10y=20
10y=-6x+20
y=-6/10x+20/10
y=-3/5x+2

5x-3y=21
-3y=21-5x
y=21/-3+-5/-3x
y=3/5x-7


Two lines are Perpendicular

Answer 2

Perpendicular

Explanation:

General equation of line:
`y=mx+c`

Line 1: 6x+10y=20

Convert in general equation

`10y = 20-6x`

`y = (20-6x)/(10)`

`y =2-(6)/(10)x`

`y =2-(3)/(5)x`

Line 2: 5x-3y=21

Convert in general equation

`5x-21=3y`

`(5x-21)/(3)=3y`

`(5)/(3)x-7=3y`

if slopes are equal then the lines are parallel

If the product of slopes is -1 then they are perpendicular

Since
`(-3)/(5) \\eq (5)/(3)`

So, lines are not parallel

`(-3)/(5) * (5)/(3)`

`-1`

Since the product of slopes is -1

Hence the given lines are perpendicular