Two functions, y = |x - 3| and 3x + 3y = 27, are graphed on the

same set of axes. Which statement is true about the solution to the

system of equations?

(1) (3,0) is the solution to the system because it satisfies the equation

y = |x - 3|.

(2) (9,0) is the solution to the system because it satisfies the equation

3x + 3y = 27.

(3) (6,3) is the solution to the system because it satisfies both equations.

(4) (3,0), (9,0), and (6,3) are the solutions to the system of equations

because they all satisfy at least one of the equations.

y = |x - 3|

3x + 3y = 27

3x + 3|x - 3| = 27

3x + 3|x - 3| = ±27

3x + 3|x - 3| = 27 or 3x + 3|x - 3| = - 27

3x + 3 (x - 3) = 27 or 3x + 3 (x - 3) = - 27

3x + 3 (x) - 3 (3) = 27 or 3x + 3 (x) - 3 (3) = - 27

3x + 3x - 9 = 27 or 3x + 3x - 9 = - 27

6x - 9 = 27 or 6x - 9 = - 27

+ 9 + 9 + 9 + 9

6x = 36 or 6x = - 18

6 6 6 6

x = 6 or x = - 3

y = |x - 3| or y = |x - 3|

y = |6 - 3| or y = |-3 - 3|

y = |3| or y = |-6|

y = 3 or y = 6

(x, y) = (6, 3) or (x, y) = (-3, 6)

The two systems of equations of the graph is only equal to (6, 3). It is not equal to (-3, 6) because one of the systems of equations - y = |x - 3| - only has one solution to the function. So the answer to the problem is 3 - (6, 3) is the solution to the system because it satisfies both equations.