Question

he tables represent two linear functions in a system.

A 2 column table with 5 rows. The first column, x, has the entries, negative 6, negative 3, 0, 3. The second column, y, has the entries, negative 22, negative 10, 2, 14. A 2 column table with 5 rows. The first column, x, has the entries, negative 6, negative 3, 0, 3. The second column, y, has the entries, negative 30, negative 21, negative 12, negative 3.
What is the solution to this system?

(negative StartFraction 13 over 3 EndFraction, negative 25)
(negative StartFraction 14 over 3 EndFraction, negative 54)
(–13, –50)
(–14, –54)

Answer 1

Find each line's equation from the table.

Line 1: y increases by 12 when x increases by 3, so slope = 4. At x=0, y=2, so y = 4x + 2.
Line 2: y increases by 9 when x increases by 3, so slope = 3. At x=0, y = -12, so y = 3x - 12.

Solve 4x + 2 = 3x - 12 → x = -14. Then y = 4(-14)+2 = -54.

Solution: (–14, –54).