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2 years ago

Number 27.

Mathematics

1 answer:

atroni [7]2 years ago

5 0

<h3>Answer:</h3>

none of these has "no solution"

<h3>Explanation:</h3>

A. The solution is (8/3, 3)

B. The second equation is -1/2 times the first, so these describe the same line. The system has an <em>infinite number of solutions</em>.

C. The solution is (-4, -2)

D. The solution is (4, -2)

E. The second equation is 2 times the first, so these describe the same line. The system has an <em>infinite number of solutions</em>.

_____

A system of equations will have "no solution" when it describes parallel lines—lines that do not intersect. In standard form, such equations are recognizable by their different constants. For example,

3x -4y = -4
3x -4y = 20 . . . . . . 20 is different from -4

have different constants, so the equations describe parallel lines.

We could multiply one of these by -2 and the system would still be "inconsistent"—having no solution.

3x -4y = -4
-6x +8y = -40

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<u>SOLUTION: </u>

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