3. how many solutions does the system of equations have? 4x = -12y + 16 and x + 3y = 4 a.) one b.) two c.) infinitely many d.) none 4.) how many solutions does the system of equations have? y = 6x + 2 and y = 6x + 4 a.) one b.) two c.) infinite d.) none

  3. c) infinitely many

  4. d) none

Step-by-step explanation:

Rewriting the first equation by dividing by 4 and adding 3y gives ...

  4x = -12y +16 . . . . .given

  x = -3y +4 . . . . . . . divide by 4

  x +3y = 4 . . . . . . . . add 3y

This is identical to the second equation, so both equations describe the same line. Each of the points on one line is also a point on the other line, so they intersect in an infinite number of places.

There are infinitely many solutions.

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If you subtract the first equation from the second, you get ...

  (y) -(y) = (6x +4) -(6x +2)

  0 = 2

This is always false. There are no values of the variables that will make this true.

There are no solutions.

no

step-by-step explanation:

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