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saveliy_v [14]
2 years ago
6

Line A is represented by the following equation: x + y = 2

Mathematics
1 answer:
Orlov [11]2 years ago
3 0

Answer:

ax+ay=k; a\ne0, k\ne2a; line D in the options.

Step-by-step explanation:

The set of equations has no solutions if the two lines are parallel. A quick way to create a parallel line is to solve for y, put it in slope-intercept form. Else, as long as the cofficient of x and y are in the same ratio (in this case 1:1), the two lines are parallel, you just have to be careful not to pick the same line again!

The condition a\ne 0 makes sure you are still getting lines (else you would get rid of both x and y); the condition k\ne 2a makes sure you're not picking line A again, just written in a different form.

Now that we have the options:

A and C have a different ratio for the coefficient of x and y (2:1 and 1:2) so are not good.

Choice B is just a more complicated way to write the same line, you can see by dividing both sides by 2 and get back x+y=2.

Line D is correct.

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