Question

Determine the solution to the system of equations graphed below and explain

G(x)=3x+2
F(x)= |x-4|+2

Answer 1

If x - 4 ≥ 0, then |x - 4| = x - 4, so

G(x) = F(x) ⇒ 3x + 2 = (x - 4) + 2

⇒ 3x + 2 = x - 2

⇒ 2x = -4

⇒ x = -2

Otherwise, if x - 4 < 0, then |x - 4| = -(x - 4), so

G(x) = F(x) ⇒ 3x + 2 = -(x - 4) + 2

⇒ 3x + 2 = -x + 6

⇒ 4x = 4

⇒ x = 1

However,

• when x = -2, we have

G(-2) = 3(-2) + 2 = -4

F(-2) = |-2 - 4| + 2 = 8

• when x = 1, we have

G(1) = 3(1) + 2 = 5

F(1) = |1 - 4| + 2 = 5

so only x = 1 is a solution to G(x) = F(x).