Which equation can pair with 3x 4y = 8 to create a consistent and independent system? 6x 8y=16-3x-4y=-66x-3y=2-3x-4y=-8

Answer : 6x - 3y=2

When system of equations that has only one solution then they are said to  be consistent and independent system.

We need to check with every option to see which equations gives us one solution.

Given : 3x + 4y = 8

A : 6x + 8y=16

Multiply 3x + 4y = 8 by -2, we will get -6x -8x = -16

-6x -8x = -16

6x + 8y=16

------------------ add both equation

0. So option A does not gives us solution

B)-3x-4y=-6

3x + 4y = 8

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0 = 2.   So option B does not gives us solution.

c) 6x-3y=2

(3x + 4y = 8) * -2

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6x - 3y = 2

-6x -8y = -16

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-11y = -14

y =

Plug in x value and solve for y

6x - 3( ) = 2

6x - ( ) = 2

6x =  

x=  

We got solution when we solve the above equations

So 6x - 3y=2 can pair with 3x + 4y = 8 to create a consistent and independent system.

the answer would be c