Question

Which system of equations below has exactly one solution?

y = –8x – 6 and y = –8x + 6

y = –8x – 6 and One-halfy = –4x – 3

y = –8x – 6 and y = 8x – 6

y = –8x – 6 and –y = 8x + 6

Answer 1

y=-8x-6 and

y=8x-6 has exactly one solution

Explanation:

Answer 2

The given system of equations
`y=-8x-6` and

`y=8x-6` has exactly one solution

Explanation:

Given that the system of equations
`y=-8x-6\hfill (1)` and

`y=8x-6\hfill (2)` has exactly one solution

For :

Now to show that the given system of equations has exactly one solution :

Solving the given equations (1) and (2) to get solution

Adding the equations (1) and (2) we get

`y=-8x-6`

`y=8x-6`

______________

`2y=0-12`

`y=-(12)/(2)`

`=-6`

Therefore the value of is y=-6

Substitute the value of y in equation (1) we have

`-6=-8x-6`

`-8x-6+6=0`

`-8x+0=0`

`-8x=0`

`x=-(0)/(8)`

`=0`

Therefore the value of x is x=0

Therefore it has exactly one solution is (0,-6)

Therefore the given system of equations
`y=-8x-6` and

`y=8x-6` has exactly one solutione given system of equations has exactly one solution