Question

Explain to your guardian how you would solve the below problem

step by step. Solve the system y = 2x + 6 and 3y = 6x + 18 by using graph paper or graphing technology.
What is the solution to the system? Feel free to submit graphs.

Answer 1

infinite solutions

Explanation:

y = 2x + 6

when x = 0, y = (2 x 0) + 6 = 6 ⇒ (0, 6)

when y = 0, 0 = 2x + 6 ⇒ x = 3 ⇒ (3, 0)

Plot the two points and draw a line through them

3y = 6x + 18

divide everything by 3 ⇒ y = 2x + 6

Therefore, y = 2x + 6 equals 3y = 6x + 18

So the lines overlap (produce the same graph)

Therefore, the system will have infinite solutions