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

  –y – 2x = 6 . . . choice 1

Step-by-step 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.

First one: -y - 2x = 6

Step-by-step 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

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right

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