Question

Use the graph. Which system of equations is consistent and dependent?

Answer 1

Answer:

Option A

Step-by-step explanation:

A system of equations is consistent when it has at least one solution. If the system is represented by lines it's not consistent if the lines that represent it never intercept each other. Now, if a system is consistent and has an infinite number of solutions then we say that is also dependent. When you graph the equations of a consistent and dependent system those graph must all be the same. Let's use this to find the answer. As you can see the graph of option B is composed of two different lines that we can identify so this is not a dependent system. The same happens with C and D, the graph of each of these systems is composed of two lines instead of one. Now let's see if A is dependent. We have the following equations:

y=2x+1

y-1=2x

If the second equation can be rewritten as the first one then they represent the same line and the system is dependent. Let's take the second equation and add 1 to both sides:

y-1+1=2x+1

y=2x+1

Which is exactly the same equation as the first one. Then these two equations represent the same line. Then the answer is option A.

Hence, the correct answer is Option A