Question

The table represents a system of equations.



x y Subscript 1 Baseline y Subscript 2 Baseline
0 negative 12 8
4 negative 6 10
8 0 12
12 6 14
16 12 16
20 18 18
24 24 20

Question
What is the solution to this system of equations?

Answer options with 5 options
A.
the point 0 comma negative 12

B.
the point 8 comma 0

C.
the point 8 comma 12

D.
the point 18 comma 18

E.
the point 20 comma 18

Answer 1

To find the solution to the system of equations represented in the table, we need to look for the point where two equations (corresponding to \(y_1\) and \(y_2\)) are equal.

From the table:

- At \(x = 0\): \(y_1 = -12\), \(y_2 = 8\) (not equal)
- At \(x = 4\): \(y_1 = -6\), \(y_2 = 10\) (not equal)
- At \(x = 8\): \(y_1 = 0\), \(y_2 = 12\) (not equal)
- At \(x = 12\): \(y_1 = 6\), \(y_2 = 14\) (not equal)
- At \(x = 16\): \(y_1 = 12\), \(y_2 = 16\) (not equal)
- At \(x = 20\): \(y_1 = 18\), \(y_2 = 18\) (equal)

The only point in the table where \(y_1\) equals \(y_2\) is at \(x = 20\), leading to the solution:

The point is \( (20, 18) \).

Thus, the correct answer is:

**E. the point 20 comma 18**.