Question

Show your solution and answer the questions​

Answer 1

9514 1404 393

Answer:

1. inconsistent; no solution
2. consistent and independent; (x, y) = (-2.5, 0)
3. consistent and independent; (x, y) = (4/5, 2/5)

Explanation:

1. Dividing the second equation by -3, we find it to be ...

x -y = -1/3

This is inconsistent with the first equation. There is no solution.

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2. Dividing the second equation by -3 gives ...

2x +2y = -5

This is consistent and independent with respect to the first equation. It tells you immediately that y=0, so x = -5/2. The solution is (-2.5, 0).

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3. The first equation has a slope of 1/2. The second equation has a slope of -2, so the equations are consistent and independent. Substituting for y in the second equation, you have 5/2x = 2, so x = 4/5. The first equation tells you y is half that, so y = 2/5. The solution is (4/5, 2/5).

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The attachments show the graphs (and solutions) of the systems of equations.