Question

Circle all systems of equations that have NO solutions. A. y = 5 – 3x y = -3x + 4 B. y = 4x – 1 4y = 16x – 4 C. 5x – 2y = 3 10x – 4y = 6 D. 3x + 7y = 42 6x + 14 y = 50 E. y = 5 + 2x y = 5x + 2

Answer 1

To determine if a system of equation have solution you have to determine if the slope (m) is equal or diferent.

If the slope is the same it has NO solution

If the slope is different has a solution

If the equations are equivalents have infinite solutions

To determine the slope the equation must be is the form:

`y=mx+b`

Then

A.

y = 5 – 3x

In this equation the slope is m = -3

y = -3x + 4

In this equation the slope is m= - 3

The system has NO solution

B.

y = 4x – 1

m= 4

4y = 16x – 4

You need to simplify the equation, as follow:

`(4)/(4)y=(16)/(4)x-(4)/(4)`
`y=4x-1`

Then the equation are the same it means the system has infinited solutions.

C.

5x – 2y = 3

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

m= 5/2

10x – 4y = 6

`-4y=6-10x`
`y=-(6)/(4)+(10)/(4)x`

Simplify:

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

Then the equation are the same it means the system has infinited solutions.

D.

3x + 7y = 42

`7y=42-3x`
`y=(42)/(7)-(3)/(7)x`
`y=6-(3)/(7)x`

m= -3/7

6x + 14 y = 50

`14y=50-6x`
`y=(50)/(14)-(6)/(14)x`
`y=(25)/(7)-(3)/(7)x`

m= -3/7

The system has NO solution

E.

y = 5 + 2x

m= 2

y = 5x + 2​

m= 5

The system has one solution

Then the systems that have NO solution are: A and D