Question

Consider the equation 2y – 4x = 12. Which equation, when graphed with the given equation, will form a system with one solution? –y – 2x = 6 –y + 2x = 12 y = 2x + 6 y = 2x + 12

Answer 1

First one: -y - 2x = 6

Explanation:

Coplanar parallel lines never intersect

Given line:

2y - 4x = 12

2y = 4x + 12

y = 2x + 6

Has a slope of 2

Search for the line which doesn't have a slope of 2

-y - 2x = 6

y = -2x - 6

Has a slope of -2, so this line will intersect the given line at one point. Hence one solution

Answer 2

–y – 2x = 6 . . . choice 1

Explanation:

Consider the system obtained using the other answer choices:

-y +2x = 12 . . . choice 2

The result of multiplying the given equation by -1/2 is ...

-y +2x = -6 . . . . a line parallel to that of answer choice 2. The system would have no solution

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y = 2x +6 . . . choice 3

Solve the given equation for y by adding 4x and dividing by 2. That will give ...

y = 2x +6 . . . . a line identical to that of answer choice 3. The system would have an infinite number of solutions.

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y = 2x +12 . . . choice 4

As we found in the previous discussion, the given line can be written as ...

y = 2x + 6 . . . . a line parallel to that of answer choice 4. The system would have no solution.

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The attached graph shows the given line and that of answer choice 1.