SOLUTION: Which of the following equations would not be consistent with 3y - 4x = 7? A. - 8x = 6y - 14 B. 12y = - 9x + 28 C. - 16x + 28 = 12y D. - 4x - 3y - 7 = 0 E. - 56 - 24y = - 32x

Algebra ->  Rational-functions -> SOLUTION: Which of the following equations would not be consistent with 3y - 4x = 7? A. - 8x = 6y - 14 B. 12y = - 9x + 28 C. - 16x + 28 = 12y D. - 4x - 3y - 7 = 0 E. - 56 - 24y = - 32x      Log On


   

Question 1152631: Which of the following equations would not be consistent with 3y - 4x = 7?
A. - 8x = 6y - 14
B. 12y = - 9x + 28
C. - 16x + 28 = 12y
D. - 4x - 3y - 7 = 0
E. - 56 - 24y = - 32x
Found 2 solutions by greenestamps, Edwin McCravy:
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


Find one of the choices that is equivalent to 3y - 4x = c where the constant c is something other than 7.

A. - 8x = 6y - 14 --> 6y + 8x = 14 --> 3y + 4x = 7 no...

B. 12y = - 9x + 28 --> 12y + 9x = 28 --> 4y + 3x = 28/3 no...

C. - 16x + 28 = 12y --> 12y + 16x = 28 --> 3y + 4x = 7 no...

D. - 4x - 3y - 7 = 0 --> 3y + 4x = -7 no...

E. - 56 - 24y = - 32x --> 24y - 32x = -56 --> 3y - 4x = -7 YES!

Answer choice E is not consistent with the given equation; it is impossible for 3y-4x to be equal to both 7 and -7.

Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
Which of the following equations would not be consistent with 3y - 4x = 7?
Find two points on the line which has that equation:
Let y=1, then

  3y - 4x = 7
3(1) - 4x = 7
   3 - 4x = 7
      -4x = 4
        x = -1, so (1,-1) is one point on the line whose equation is 3y - 4x = 7  


Let x=2, then

  3y - 4x = 7
3y - 4(2) = 7
   3y - 8 = 7
       3y = 15
        y = 5, so (2,5) is another point on the line whose equation is 3y - 4x = 7

Let's substitute (1,-1) and (2,5) in each of those.  If they both satisfy the
equation, the equation is compatible with 3y - 4x = 7.  But if either one of
the two points does not, then the equation is not compatible with 3y - 4x = 7.
A. - 8x = 6y - 14
Substituting (1,-1)
-8x = 6y - 14
-8(1) = 6(-1) - 14
   -8 = -6 - 14
   -8 = -20     [So (1,-1) DOES NOT satisfy it.]

So A. is NOT compatible with 3y - 4x = 7
-------------------------------------------------
B. 12y = - 9x + 28
Substituting (1,-1)
   12y = -9x + 28
12(-1) = -9(1) + 28
   -12 = -9 + 28
   -12 = 19  [So (1,-1) DOES NOT satisfy it.]

So B. is NOT compatible with 3y - 4x = 7
-------------------------------------------------
C. - 16x + 28 = 12y
Substituting (1,-1)
  -16x + 28 = 12y
-16(1) + 28 = 12(-1)
   -16 + 28 = -12
         12 = -12 [So (1,-1) DOES NOT satisfy it.]

So C. is NOT compatible with 3y - 4x = 7
-------------------------------------------------------
D. - 4x - 3y - 7 = 0
Substituting (1,-1)
      -4x - 3y - 7 = 0
 -4(1) - 3(-1) - 7 = 0
        -4 + 3 - 7 = 0
                -8 = 0 [So (1,-1) DOES NOT satisfy it.]

So D. is NOT compatible with 3y - 4x = 7
---------------------------------------------------------
E. - 56 - 24y = - 32x
Substituting (1,-1)
    -56 - 24y = -32x
 -56 - 24(-1) = -32(1)
     -56 + 24 = -32
          -32 = -32  [So (1,-1) satisfies it. So we substitute the other point.]

Substituting (2,5)
    -56 - 24y = -32x
  -56 - 24(5) = -32(2)
     -56 -120 = -64
         -176 = -32  [So (2,5) DOES NOT satisfies it.]

So E. is NOT compatible with 3y - 4x = 7

So NONE of them are compatible with 3y - 4x = 7

Edwin