Question

Line H is represented by the following equation: 2x + 2y = 8

What is most likely the equation for line K so the set of equations has infinitely many solutions?

x + 2y = 2
x + y = 4
2x + y = 6
x − y = 8

Answer 1

b

Explanation:

i did the test and got it right

Answer 2

B

Explanation:

Line H is represented by the equation:

`2x+2y=8`

And we want to find Line K such that the set of equations has infinitely many solutions.

Remember the three solution sets for linear equations:

• If the two are parallel, they have no solutions.
• If the two are not parallel, they will intersect and thus have only one solution.
• If the two are the exact same line, then they will have infinitely many solutions.

From Line H, we can divide both sides by two. This yields the equivalent equation:

`x+y=4`

Therefore, the new equation and Line H are the same line. Thus, they will have infinitely many solutions.

The answer is B.