Question

Solve the equation using elimination. Is this a consistent, inconsistent, or dependent? What is the solution

Answer 1

9514 1404 393

Answer:

  (x, y) = (-1, -3)

Step-by-step explanation:

The equations are "consistent" and "not dependent." This will be the case whenever the ratios of x- and y-coefficients are different.

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We can solve this by "elimination" by multiplying the first equation by -4 and adding the result of the second equation being multiplied by 7.

  -4(2x -7y) +7(7x -4y) = -4(19) +7(5)

  -8x +28y +49x -28y = -76 +35 . . . . eliminate parentheses

  41x = -41 . . . . . simplify

  x = -1 . . . . . . . divide by 41

Using the second equation, we find y to be ...

  (7x -5)/4 = y = (7(-1) -5)/4 = -12/4 = -3

So, the solution is (x, y) = (-1, -3).