Question

Which system below has no solution?

1. y = 4x and y = 2x - 3
2. y = -4x and y = 2x - 3
3. y = -4x and y = 2x + 3
4. y = -4-x and y = 2x - 3

Answer 1

First one,

y = 4^x and y = 2^ - 3

Answer 2

None of these options has "no solution"

Explanation:

we will verify each options

(1)

y = 4x and y = 2x - 3

we can set them equal and solve for x

`4x=2x-3`

`2x=-3`

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

Since, solutions exists

so, this is FALSE

(2)

y = -4x and y = 2x - 3

we can set them equal and solve for x

`-4x=2x-3`

`-6x=-3`

`x=(1)/(2)`

Since, solutions exists

so, this is FALSE

(3)

y = 4x and y = 2x+ 3

we can set them equal and solve for x

`4x=2x+3`

`2x=3`

`x=(3)/(2)`

Since, solutions exists

so, this is FALSE

(4)

y = -4-x and y = 2x - 3

we can set them equal and solve for x

`-4-x=2x-3`

`-3x=1`

`x=-(1)/(3)`

Since, solutions exists

so, this is FALSE

So, No system of equations have no solution