## 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

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

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1 week 2021-07-20T04:44:13+00:00 1 Answers 5 views 0

B

Step-by-step explanation:

Line H is represented by the equation:

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:

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